 5.5.2.1: The inverse function of the exponential function is called the ____...
 5.5.5.1: An exponential growth model has the form ________, and an exponenti...
 5.5.3.1: To evaluate a logarithm to any base, use the ________ formula.
 5.1: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.1: Polynomial and rational functions are examples of ________ functions
 5.5.4.1: To solve exponential and logarithmic equations, you can use the fol...
 5.5.2.2: The common logarithmic function has base ________ .
 5.5.5.2: A logarithmic model has the form ________ or ________.
 5.5.3.2: The changeofbase formula for base is given by ________.
 5.2: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.2: Exponential and logarithmic functions are examples of nonalgebraic ...
 5.5.4.2: . An ________ solution does not satisfy the original equation.
 5.5.2.3: The logarithmic function is called the ________ logarithmic functio...
 5.5.5.3: In probability and statistics, Gaussian models commonly represent p...
 5.5.3.3: You can consider to be a constant multiple of the constant multipli...
 5.3: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.3: You can use the ________ Property to solve simple exponential equat...
 5.5.4.3: In Exercises 36, determine whether each value is a solution (or an...
 5.5.2.4: The Inverse Properties of logarithms state that and ________.
 5.5.5.4: A logistic growth model has the form ________.
 5.5.3.4: In Exercises 46, match the property of logarithms with its name. lo...
 5.4: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.4: The exponential function is called the ________ ________ function, ...
 5.5.4.4: In Exercises 36, determine whether each value is a solution (or an...
 5.5.2.5: The OnetoOne Property of natural logarithms states that if then _...
 5.5.5.5: In Exercises 5 and 6, (a) solve for and (b) solve for t A Pert
 5.5.3.5: In Exercises 46, match the property of logarithms with its name. ln...
 5.5: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.5: To find the amount in an account after years with principal and an ...
 5.5.4.5: In Exercises 36, determine whether each value is a solution (or an...
 5.5.2.6: The domain of the natural logarithmic function is the set of ______...
 5.5.5.6: In Exercises 5 and 6, (a) solve for and (b) solve for t A P1 rnnt
 5.5.3.6: In Exercises 46, match the property of logarithms with its name. lo...
 5.6: In Exercises 16, evaluate the function at the indicated value of Ro...
 5.5.1.6: To find the amount in an account after years with principal and an ...
 5.5.4.6: In Exercises 36, determine whether each value is a solution (or an...
 5.5.2.7: In Exercises 710, write the logarithmic equation in exponential for...
 5.5.5.7: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.7: In Exercises 710, rewrite the logarithm as a ratio of (a) common lo...
 5.7: In Exercises 710, use the graph of to describe the transformation t...
 5.5.1.7: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.7: In Exercises 714, solve for x 4 32 x 16
 5.5.2.8: In Exercises 710, write the logarithmic equation in exponential for...
 5.5.5.8: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.8: In Exercises 710, rewrite the logarithm as a ratio of (a) common lo...
 5.8: In Exercises 710, use the graph of to describe the transformation t...
 5.5.1.8: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.8: In Exercises 714, solve for x 12x4 32 x
 5.5.2.9: In Exercises 710, write the logarithmic equation in exponential for...
 5.5.5.9: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.9: In Exercises 710, rewrite the logarithm as a ratio of (a) common lo...
 5.9: In Exercises 710, use the graph of to describe the transformation t...
 5.5.1.9: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.9: In Exercises 714, solve for x n x ln 2 0 x
 5.5.2.10: In Exercises 710, write the logarithmic equation in exponential for...
 5.5.5.10: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.10: In Exercises 710, rewrite the logarithm as a ratio of (a) common lo...
 5.10: In Exercises 710, use the graph of to describe the transformation t...
 5.5.1.10: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.10: In Exercises 714, solve for x x 2
 5.5.2.11: In Exercises 1114, write the exponential equation in logarithmic fo...
 5.5.5.11: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.11: In Exercises 1114, evaluate the logarithm using the changeofbase ...
 5.11: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.11: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.11: In Exercises 714, solve for x ln x 1 l
 5.5.2.12: In Exercises 1114, write the exponential equation in logarithmic fo...
 5.5.5.12: In Exercises 712, complete the table assuming continuously compound...
 5.5.3.12: In Exercises 1114, evaluate the logarithm using the changeofbase ...
 5.12: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.12: In Exercises 712, evaluate the function at the indicated value of R...
 5.5.4.12: In Exercises 714, solve for x log x 2
 5.5.2.13: In Exercises 1114, write the exponential equation in logarithmic fo...
 5.5.5.13: In Exercises 13 and 14, determine the principal that must be invest...
 5.5.3.13: In Exercises 1114, evaluate the logarithm using the changeofbase ...
 5.13: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.13: In Exercises 1316, match the exponential function with its graph. [...
 5.5.4.13: In Exercises 714, solve for x log4 x 3
 5.5.2.14: In Exercises 1114, write the exponential equation in logarithmic fo...
 5.5.5.14: In Exercises 13 and 14, determine the principal that must be invest...
 5.5.3.14: In Exercises 1114, evaluate the logarithm using the changeofbase ...
 5.14: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.14: In Exercises 1316, match the exponential function with its graph. [...
 5.5.4.14: In Exercises 714, solve for x log5 x 1
 5.5.2.15: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.15: In Exercises 15 and 16, determine the time necessary for dollars to...
 5.5.3.15: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.15: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.15: In Exercises 1316, match the exponential function with its graph. [...
 5.5.4.15: In Exercises 15 and 16, approximate the point of intersection of th...
 5.5.2.16: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.16: In Exercises 15 and 16, determine the time necessary for dollars to...
 5.5.3.16: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.16: In Exercises 1116, use a graphing utility to construct a table of v...
 5.5.1.16: In Exercises 1316, match the exponential function with its graph. [...
 5.5.4.16: In Exercises 15 and 16, approximate the point of intersection of th...
 5.5.2.17: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.17: Compound Interest Complete the table for the time (in years) necess...
 5.5.3.17: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.17: In Exercises 1720, use the OnetoOne Property to solve the equatio...
 5.5.1.17: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.17: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.18: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.18: Modeling Data Draw scatter plots of the data in Exercise 17. Use th...
 5.5.3.18: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.18: In Exercises 1720, use the OnetoOne Property to solve the equatio...
 5.5.1.18: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.18: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.19: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.19: Comparing Models If $1 is invested over a 10year period, then the ...
 5.5.3.19: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.19: In Exercises 1720, use the OnetoOne Property to solve the equatio...
 5.5.1.19: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.19: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.20: In Exercises 1520, evaluate the function at the indicated value of ...
 5.5.5.20: Comparing Models If $1 is invested over a 10year period, then the ...
 5.5.3.20: In Exercises 1520, use the properties of logarithms to rewrite and ...
 5.20: In Exercises 1720, use the OnetoOne Property to solve the equatio...
 5.5.1.20: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.20: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.21: In Exercises 2124, use a calculator to evaluate at the indicated va...
 5.5.5.21: In Exercises 2124, complete the table for the radioactive isotope. ...
 5.5.3.21: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.21: In Exercises 2124, evaluate at the indicated value of Round your re...
 5.5.1.21: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.21: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.22: In Exercises 2124, use a calculator to evaluate at the indicated va...
 5.5.5.22: In Exercises 2124, complete the table for the radioactive isotope. ...
 5.5.3.22: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.22: In Exercises 2124, evaluate at the indicated value of Round your re...
 5.5.1.22: In Exercises 1722, use a graphing utility to construct a table of v...
 5.5.4.22: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.23: In Exercises 2124, use a calculator to evaluate at the indicated va...
 5.5.5.23: In Exercises 2124, complete the table for the radioactive isotope. ...
 5.5.3.23: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.23: In Exercises 2124, evaluate at the indicated value of Round your re...
 5.5.1.23: In Exercises 2326, use the OnetoOne Property to solve the equatio...
 5.5.4.23: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.24: In Exercises 2124, use a calculator to evaluate at the indicated va...
 5.5.5.24: In Exercises 2124, complete the table for the radioactive isotope. ...
 5.5.3.24: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.24: In Exercises 2124, evaluate at the indicated value of Round your re...
 5.5.1.24: In Exercises 2326, use the OnetoOne Property to solve the equatio...
 5.5.4.24: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.25: In Exercises 2528, use the properties of logarithms to simplify the...
 5.5.5.25: In Exercises 2528, find the exponential model that fits the points ...
 5.5.3.25: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.25: In Exercises 2528, use a graphing utility to construct a table of v...
 5.5.1.25: In Exercises 2326, use the OnetoOne Property to solve the equatio...
 5.5.4.25: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.26: In Exercises 2528, use the properties of logarithms to simplify the...
 5.5.5.26: In Exercises 2528, find the exponential model that fits the points ...
 5.5.3.26: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.26: In Exercises 2528, use a graphing utility to construct a table of v...
 5.5.1.26: In Exercises 2326, use the OnetoOne Property to solve the equatio...
 5.5.4.26: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.27: In Exercises 2528, use the properties of logarithms to simplify the...
 5.5.5.27: In Exercises 2528, find the exponential model that fits the points ...
 5.5.3.27: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.27: In Exercises 2528, use a graphing utility to construct a table of v...
 5.5.1.27: In Exercises 2730, use the graph of to describe the transformation ...
 5.5.4.27: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.28: In Exercises 2528, use the properties of logarithms to simplify the...
 5.5.5.28: In Exercises 2528, find the exponential model that fits the points ...
 5.5.3.28: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.28: In Exercises 2528, use a graphing utility to construct a table of v...
 5.5.1.28: In Exercises 2730, use the graph of to describe the transformation ...
 5.5.4.28: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.29: In Exercises 2932, use the OnetoOne Property to solve the equatio...
 5.5.5.29: Population The populations (in thousands) of Horry County, South Ca...
 5.5.3.29: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.29: Waiting Times The average time between incoming calls at a switchbo...
 5.5.1.29: In Exercises 2730, use the graph of to describe the transformation ...
 5.5.4.29: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.30: In Exercises 2932, use the OnetoOne Property to solve the equatio...
 5.5.5.30: The table shows the midyear populations (in millions) of five coun...
 5.5.3.30: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.30: Depreciation After years, the value of a car that originally cost $...
 5.5.1.30: In Exercises 2730, use the graph of to describe the transformation ...
 5.5.4.30: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.31: In Exercises 2932, use the OnetoOne Property to solve the equatio...
 5.5.5.31: Website Growth The number of hits a new website receives each month...
 5.5.3.31: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.31: In Exercises 31 and 32, complete the table to determine the balance...
 5.5.1.31: In Exercises 3134, use a graphing utility to graph the exponential ...
 5.5.4.31: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.32: In Exercises 2932, use the OnetoOne Property to solve the equatio...
 5.5.5.32: Population The populations (in thousands) of Tallahassee, Florida, ...
 5.5.3.32: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.32: In Exercises 31 and 32, complete the table to determine the balance...
 5.5.1.32: In Exercises 3134, use a graphing utility to graph the exponential ...
 5.5.4.32: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.33: In Exercises 3336, sketch the graphs of and in the same coordinate ...
 5.5.5.33: Bacteria Growth The number of bacteria in a culture is increasing a...
 5.5.3.33: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.33: In Exercises 3336, write the exponential equation in logarithmic fo...
 5.5.1.33: In Exercises 3134, use a graphing utility to graph the exponential ...
 5.5.4.33: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.34: In Exercises 3336, sketch the graphs of and in the same coordinate ...
 5.5.5.34: Bacteria Growth The number of bacteria in a culture is increasing a...
 5.5.3.34: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.34: In Exercises 3336, write the exponential equation in logarithmic fo...
 5.5.1.34: In Exercises 3134, use a graphing utility to graph the exponential ...
 5.5.4.34: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.35: In Exercises 3336, sketch the graphs of and in the same coordinate ...
 5.5.5.35: Depreciation A laptop computer that costs $1150 new has a book valu...
 5.5.3.35: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.35: In Exercises 3336, write the exponential equation in logarithmic fo...
 5.5.1.35: In Exercises 3538, evaluate the function at the indicated value of ...
 5.5.4.35: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.4.36: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.36: In Exercises 3336, sketch the graphs of and in the same coordinate ...
 5.5.5.36: Learning Curve The management at a plastics factory has found that ...
 5.5.3.36: In Exercises 2136, find the exact value of the logarithmic expressi...
 5.36: In Exercises 3336, write the exponential equation in logarithmic fo...
 5.5.1.36: In Exercises 3538, evaluate the function at the indicated value of ...
 5.5.4.37: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.37: In Exercises 3740, use the graph of to match the given function wit...
 5.5.5.37: Carbon Dating (a) The ratio of carbon 14 to carbon 12 in a piece of...
 5.5.3.37: In Exercises 3758, use the properties of logarithms to expand the e...
 5.37: In Exercises 3740, evaluate the function at the indicated value of ...
 5.5.1.37: In Exercises 3538, evaluate the function at the indicated value of ...
 5.5.4.38: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.38: In Exercises 3740, use the graph of to match the given function wit...
 5.5.5.38: Radioactive Decay Carbon 14 dating assumes that the carbon dioxide ...
 5.5.3.38: In Exercises 3758, use the properties of logarithms to expand the e...
 5.38: In Exercises 3740, evaluate the function at the indicated value of ...
 5.5.1.38: In Exercises 3538, evaluate the function at the indicated value of ...
 5.5.4.39: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.39: In Exercises 3740, use the graph of to match the given function wit...
 5.5.5.39: IQ Scores The IQ scores for a sample of a class of returning adult ...
 5.5.3.39: In Exercises 3758, use the properties of logarithms to expand the e...
 5.39: In Exercises 3740, evaluate the function at the indicated value of ...
 5.5.1.39: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.40: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.40: In Exercises 3740, use the graph of to match the given function wit...
 5.5.5.40: Education The amount of time (in hours per week) a student utilizes...
 5.5.3.40: In Exercises 3758, use the properties of logarithms to expand the e...
 5.40: In Exercises 3740, evaluate the function at the indicated value of ...
 5.5.1.40: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.41: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.41: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.41: . Cell Sites A cell site is a site where electronic communications ...
 5.5.3.41: In Exercises 3758, use the properties of logarithms to expand the e...
 5.41: In Exercises 4144, use the OnetoOne Property to solve the equatio...
 5.5.1.41: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.42: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.42: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.42: Population The populations (in thousands) of a city from 2000 throu...
 5.5.3.42: In Exercises 3758, use the properties of logarithms to expand the e...
 5.42: In Exercises 4144, use the OnetoOne Property to solve the equatio...
 5.5.1.42: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.43: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.43: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.43: Population Growth A conservation organization released 100 animals ...
 5.5.3.43: In Exercises 3758, use the properties of logarithms to expand the e...
 5.43: In Exercises 4144, use the OnetoOne Property to solve the equatio...
 5.5.1.43: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.44: In Exercises 1744, solve the exponential equation algebraically. Ap...
 5.5.2.44: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.44: Sales After discontinuing all advertising for a tool kit in 2007, t...
 5.5.3.44: In Exercises 3758, use the properties of logarithms to expand the e...
 5.44: In Exercises 4144, use the OnetoOne Property to solve the equatio...
 5.5.1.44: In Exercises 39 44, use a graphing utility to construct a table of ...
 5.5.4.45: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.45: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.45: In Exercises 45 and 46, use the Richter scale for measuring the mag...
 5.5.3.45: In Exercises 3758, use the properties of logarithms to expand the e...
 5.45: In Exercises 4548, find the domain, intercept, and vertical asympt...
 5.5.1.45: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.46: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.46: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.46: In Exercises 45 and 46, use the Richter scale for measuring the mag...
 5.5.3.46: In Exercises 3758, use the properties of logarithms to expand the e...
 5.46: In Exercises 4548, find the domain, intercept, and vertical asympt...
 5.5.1.46: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.47: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.47: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.47: In Exercises 4750, use the following information for determining so...
 5.5.3.47: In Exercises 3758, use the properties of logarithms to expand the e...
 5.47: In Exercises 4548, find the domain, intercept, and vertical asympt...
 5.5.1.47: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.48: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.48: In Exercises 4148, find the domain, intercept, and vertical asympt...
 5.5.5.48: In Exercises 4750, use the following information for determining so...
 5.5.3.48: In Exercises 3758, use the properties of logarithms to expand the e...
 5.48: In Exercises 4548, find the domain, intercept, and vertical asympt...
 5.5.1.48: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.49: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.49: In Exercises 4952, write the logarithmic equation in exponential fo...
 5.5.5.49: In Exercises 4750, use the following information for determining so...
 5.5.3.49: In Exercises 3758, use the properties of logarithms to expand the e...
 5.49: In Exercises 4952, use a calculator to evaluate the function at the...
 5.5.1.49: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.50: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.50: In Exercises 4952, write the logarithmic equation in exponential fo...
 5.5.5.50: In Exercises 4750, use the following information for determining so...
 5.5.3.50: In Exercises 3758, use the properties of logarithms to expand the e...
 5.50: In Exercises 4952, use a calculator to evaluate the function at the...
 5.5.1.50: In Exercises 45 50, use a graphing utility to graph the exponential...
 5.5.4.51: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.51: In Exercises 4952, write the logarithmic equation in exponential fo...
 5.5.5.51: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.51: In Exercises 3758, use the properties of logarithms to expand the e...
 5.51: In Exercises 4952, use a calculator to evaluate the function at the...
 5.5.1.51: In Exercises 5154, use the OnetoOne Property to solve the equatio...
 5.5.4.52: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.52: In Exercises 4952, write the logarithmic equation in exponential fo...
 5.5.5.52: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.52: In Exercises 3758, use the properties of logarithms to expand the e...
 5.52: In Exercises 4952, use a calculator to evaluate the function at the...
 5.5.1.52: In Exercises 5154, use the OnetoOne Property to solve the equatio...
 5.5.4.53: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.53: In Exercises 5356, write the exponential equation in logarithmic fo...
 5.5.5.53: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.53: In Exercises 3758, use the properties of logarithms to expand the e...
 5.53: In Exercises 5356, find the domain, intercept, and vertical asympt...
 5.5.1.53: In Exercises 5154, use the OnetoOne Property to solve the equatio...
 5.5.4.54: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.54: In Exercises 5356, write the exponential equation in logarithmic fo...
 5.5.5.54: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.54: In Exercises 3758, use the properties of logarithms to expand the e...
 5.54: In Exercises 5356, find the domain, intercept, and vertical asympt...
 5.5.1.54: In Exercises 5154, use the OnetoOne Property to solve the equatio...
 5.5.4.55: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.55: In Exercises 5356, write the exponential equation in logarithmic fo...
 5.5.5.55: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.55: In Exercises 3758, use the properties of logarithms to expand the e...
 5.55: In Exercises 5356, find the domain, intercept, and vertical asympt...
 5.5.1.55: In Exercises 5558, complete the table to determine the balance for ...
 5.5.4.56: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.56: In Exercises 5356, write the exponential equation in logarithmic fo...
 5.5.5.56: In Exercises 5156, use the acidity model given by where acidity (pH...
 5.5.3.56: In Exercises 3758, use the properties of logarithms to expand the e...
 5.56: In Exercises 5356, find the domain, intercept, and vertical asympt...
 5.5.1.56: In Exercises 5558, complete the table to determine the balance for ...
 5.5.4.57: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.57: In Exercises 5760, use a calculator to evaluate the function at the...
 5.5.5.57: Forensics At 8:30 A.M., a coroner went to the home of a person who ...
 5.5.3.57: In Exercises 3758, use the properties of logarithms to expand the e...
 5.57: Antler Spread The antler spread (in inches) and shoulder height (in...
 5.5.1.57: In Exercises 5558, complete the table to determine the balance for ...
 5.5.4.58: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.58: In Exercises 5760, use a calculator to evaluate the function at the...
 5.5.5.58: Home Mortgage A $120,000 home mortgage for 30 years at has a monthl...
 5.5.3.58: In Exercises 3758, use the properties of logarithms to expand the e...
 5.58: Snow Removal The number of miles of roads cleared of snow is approx...
 5.5.1.58: In Exercises 5558, complete the table to determine the balance for ...
 5.5.4.59: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.59: In Exercises 5760, use a calculator to evaluate the function at the...
 5.5.5.59: . Home Mortgage The total interest paid on a home mortgage of dolla...
 5.5.3.59: In Exercises 5966, approximate the logarithm using the properties o...
 5.59: In Exercises 5962, evaluate the logarithm using the changeofbase ...
 5.5.1.59: In Exercises 5962, complete the table to determine the balance for ...
 5.5.4.60: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.60: In Exercises 5760, use a calculator to evaluate the function at the...
 5.5.5.60: Data Analysis The table shows the time (in seconds) required for a ...
 5.5.3.60: In Exercises 5966, approximate the logarithm using the properties o...
 5.60: In Exercises 5962, evaluate the logarithm using the changeofbase ...
 5.5.1.60: In Exercises 5962, complete the table to determine the balance for ...
 5.5.4.61: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.61: In Exercises 6164, evaluate at the indicated value of without using...
 5.5.5.61: In Exercises 6164, determine whether the statement is true or false...
 5.5.3.61: In Exercises 5966, approximate the logarithm using the properties o...
 5.61: In Exercises 5962, evaluate the logarithm using the changeofbase ...
 5.5.1.61: In Exercises 5962, complete the table to determine the balance for ...
 5.5.4.62: In Exercises 4562, solve the logarithmic equation algebraically. Ap...
 5.5.2.62: In Exercises 6164, evaluate at the indicated value of without using...
 5.5.5.62: In Exercises 6164, determine whether the statement is true or false...
 5.5.3.62: In Exercises 5966, approximate the logarithm using the properties o...
 5.62: In Exercises 5962, evaluate the logarithm using the changeofbase ...
 5.5.1.62: In Exercises 5962, complete the table to determine the balance for ...
 5.5.4.63: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.63: In Exercises 6164, evaluate at the indicated value of without using...
 5.5.5.63: In Exercises 6164, determine whether the statement is true or false...
 5.5.3.63: In Exercises 5966, approximate the logarithm using the properties o...
 5.63: In Exercises 6366, use the properties of logarithms to rewrite and ...
 5.5.1.63: Trust Fund On the day of a childs birth, a parent deposits $30,000 ...
 5.5.1.64: Trust Fund A philanthropist deposits $5000 in a trust fund that pay...
 5.5.4.64: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.64: In Exercises 6164, evaluate at the indicated value of without using...
 5.5.5.64: In Exercises 6164, determine whether the statement is true or false...
 5.5.3.64: In Exercises 5966, approximate the logarithm using the properties o...
 5.64: In Exercises 6366, use the properties of logarithms to rewrite and ...
 5.5.1.65: Inflation Assuming that the annual rate of inflation averages 4% ov...
 5.5.4.65: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.65: In Exercises 6568, find the domain, intercept, and vertical asympt...
 5.5.5.65: Writing Use your schools library, the Internet, or some other refer...
 5.5.3.65: In Exercises 5966, approximate the logarithm using the properties o...
 5.65: In Exercises 6366, use the properties of logarithms to rewrite and ...
 5.5.1.66: Computer Virus The number of computers infected by a virus increase...
 5.5.4.66: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.66: In Exercises 6568, find the domain, intercept, and vertical asympt...
 5.5.5.66: HOW DO YOU SEE IT? Identify each model as exponential growth, expon...
 5.5.3.66: In Exercises 5966, approximate the logarithm using the properties o...
 5.66: In Exercises 6366, use the properties of logarithms to rewrite and ...
 5.5.1.67: Population Growth The projected populations of the United States fo...
 5.5.4.67: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.67: In Exercises 6568, find the domain, intercept, and vertical asympt...
 5.5.3.67: In Exercises 6782, condense the expression to the logarithm of a si...
 5.67: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.68: Population The populations (in millions) of Italy from 2000 through...
 5.5.4.68: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.68: In Exercises 6568, find the domain, intercept, and vertical asympt...
 5.5.3.68: In Exercises 6782, condense the expression to the logarithm of a si...
 5.68: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.69: Radioactive Decay Let represent a mass of radioactive plutonium (in...
 5.5.4.69: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.69: In Exercises 6972, use a graphing utility to graph the function. Be...
 5.5.3.69: In Exercises 6782, condense the expression to the logarithm of a si...
 5.69: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.70: Radioactive Decay Let represent a mass of carbon (in grams), whose ...
 5.5.4.70: In Exercises 6370, use a graphing utility to graph and solve the eq...
 5.5.2.70: In Exercises 6972, use a graphing utility to graph the function. Be...
 5.5.3.70: In Exercises 6782, condense the expression to the logarithm of a si...
 5.70: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.71: Depreciation After years, the value of a wheelchair conversion van ...
 5.5.4.71: In Exercises 71 and 72, you invest $2500 in an account at interest ...
 5.5.2.71: In Exercises 6972, use a graphing utility to graph the function. Be...
 5.5.3.71: In Exercises 6782, condense the expression to the logarithm of a si...
 5.71: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.72: Immediately following an injection, the concentration of a drug in ...
 5.5.4.72: In Exercises 71 and 72, you invest $2500 in an account at interest ...
 5.5.2.72: In Exercises 6972, use a graphing utility to graph the function. Be...
 5.5.3.72: In Exercises 6782, condense the expression to the logarithm of a si...
 5.72: In Exercises 6772, use the properties of logarithms to expand the e...
 5.5.1.73: In Exercises 73 and 74, determine whether the statement is true or ...
 5.5.4.73: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.73: In Exercises 7376, use the OnetoOne Property to solve the equatio...
 5.5.3.73: In Exercises 6782, condense the expression to the logarithm of a si...
 5.73: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.74: In Exercises 73 and 74, determine whether the statement is true or ...
 5.5.4.74: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.74: In Exercises 7376, use the OnetoOne Property to solve the equatio...
 5.5.3.74: In Exercises 6782, condense the expression to the logarithm of a si...
 5.74: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.75: In Exercises 7578, use properties of exponents to determine which f...
 5.5.4.75: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.75: In Exercises 7376, use the OnetoOne Property to solve the equatio...
 5.5.3.75: In Exercises 6782, condense the expression to the logarithm of a si...
 5.75: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.76: In Exercises 7578, use properties of exponents to determine which f...
 5.5.4.76: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.76: In Exercises 7376, use the OnetoOne Property to solve the equatio...
 5.5.3.76: In Exercises 6782, condense the expression to the logarithm of a si...
 5.76: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.77: In Exercises 7578, use properties of exponents to determine which f...
 5.5.4.77: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.77: Monthly Payment The model approximates the length of a home mortgag...
 5.5.3.77: In Exercises 6782, condense the expression to the logarithm of a si...
 5.77: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.78: In Exercises 7578, use properties of exponents to determine which f...
 5.5.4.78: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.78: Wireless Only The percents of households in the United States with ...
 5.5.3.78: In Exercises 6782, condense the expression to the logarithm of a si...
 5.78: In Exercises 7378, condense the expression to the logarithm of a si...
 5.5.1.79: Solving Inequalities Graph the functions and and use the graphs to ...
 5.5.4.79: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.79: Population The time (in years) for the world population to double w...
 5.5.3.79: In Exercises 6782, condense the expression to the logarithm of a si...
 5.79: Climb Rate The time (in minutes) for a small plane to climb to an a...
 5.5.1.80: Graphical Analysis Use a graphing utility to graph each function. U...
 5.5.4.80: In Exercises 7380, solve the equation algebraically. Round your res...
 5.5.2.80: Compound Interest A principal invested at and compounded continuous...
 5.5.3.80: In Exercises 6782, condense the expression to the logarithm of a si...
 5.80: Human Memory Model Students in a learning theory study took an exam...
 5.5.1.81: Graphical Analysis Use a graphing utility to graph and in the same ...
 5.5.4.81: Average Heights The percent of American males between the ages of 2...
 5.5.2.81: Students in a mathematics class took an exam and then took a retest...
 5.5.3.81: In Exercises 6782, condense the expression to the logarithm of a si...
 5.81: In Exercises 8186, solve for x 5 216 x 125
 5.5.1.82: Graphical Analysis Use a graphing utility to graph and in the same ...
 5.5.4.82: U.S. Currency The values (in billions of dollars) of U.S. currency ...
 5.5.2.82: Sound Intensity The relationship between the number of decibels and...
 5.5.3.82: In Exercises 6782, condense the expression to the logarithm of a si...
 5.82: In Exercises 8186, solve for x 6x 1 5 216
 5.5.1.83: Graphical Analysis Use a graphing utility to graph each pair of fun...
 5.5.4.83: The number of trees of a given species per acre is approximated by ...
 5.5.2.83: In Exercises 83 and 84, determine whether the statement is true or ...
 5.5.3.83: In Exercises 83 and 84, compare the logarithmic quantities. If two ...
 5.83: In Exercises 8186, solve for x e x 1 x 36
 5.5.1.84: HOW DO YOU SEE IT? The figure shows the graphs of and Match each fu...
 5.5.4.84: Demand The demand equation for a smart phone is Find the demand for...
 5.5.2.84: In Exercises 83 and 84, determine whether the statement is true or ...
 5.5.3.84: In Exercises 83 and 84, compare the logarithmic quantities. If two ...
 5.84: In Exercises 8186, solve for x log6 e x 1
 5.5.1.85: Think About It Which functions are exponential? 3x 3x 2 3x 2x
 5.5.4.85: Automobiles Engineers design automobiles with crumple zones that he...
 5.5.2.85: Graphical Analysis Use a graphing utility to graph and in the same ...
 5.5.3.85: In Exercises 8588, use the following information. The relationship ...
 5.85: In Exercises 8186, solve for x ln x 4
 5.5.1.86: Compound Interest Use the formula to calculate the balance of an in...
 5.5.4.86: Data Analysis An object at a temperature of was removed from a furn...
 5.5.2.86: Limit of a Function (a) Complete the table for the function (b) Use...
 5.5.3.86: In Exercises 8588, use the following information. The relationship ...
 5.86: In Exercises 8186, solve for x ln x 1.6
 5.5.4.87: In Exercises 8790, rewrite each verbal statement as an equation. Th...
 5.5.2.87: Think About It A student obtained the following table of values by ...
 5.5.3.87: In Exercises 8588, use the following information. The relationship ...
 5.87: In Exercises 8790, solve the exponential equation algebraically. Ap...
 5.5.4.88: In Exercises 8790, rewrite each verbal statement as an equation. Th...
 5.5.2.88: HOW DO YOU SEE IT? The figure shows the graphs of and [The graphs a...
 5.5.3.88: In Exercises 8588, use the following information. The relationship ...
 5.88: In Exercises 8790, solve the exponential equation algebraically. Ap...
 5.5.4.89: In Exercises 8790, rewrite each verbal statement as an equation. Th...
 5.5.2.89: Writing Explain why is defined only for 0 < a < 1 and a > 1
 5.5.3.89: In Exercises 8992, find a logarithmic equation that relates and Exp...
 5.89: In Exercises 8790, solve the exponential equation algebraically. Ap...
 5.5.4.90: In Exercises 8790, rewrite each verbal statement as an equation. Th...
 5.5.3.90: In Exercises 8992, find a logarithmic equation that relates and Exp...
 5.90: In Exercises 8790, solve the exponential equation algebraically. Ap...
 5.5.4.91: Think About It Is it possible for a logarithmic equation to have mo...
 5.5.3.91: In Exercises 8992, find a logarithmic equation that relates and Exp...
 5.91: In Exercises 91 and 92, use a graphing utility to graph and solve t...
 5.5.4.92: HOW DO YOU SEE IT? Solving algebraically, the solutions appear to b...
 5.5.3.92: In Exercises 8992, find a logarithmic equation that relates and Exp...
 5.92: In Exercises 91 and 92, use a graphing utility to graph and solve t...
 5.5.4.93: Finance You are investing dollars at an annual interest rate of com...
 5.5.3.93: Galloping Speeds of Animals Fourlegged animals run with two differ...
 5.93: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.4.94: Think About It Are the times required for the investments in Exerci...
 5.5.3.94: Nail Length The approximate lengths and diameters (in inches) of co...
 5.94: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.4.95: Effective Yield The effective yield of an investment plan is the pe...
 5.5.3.95: Comparing Models A cup of water at an initial temperature of is pla...
 5.95: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.4.96: Graphical Analysis Let and where (a) Let and use a graphing utility...
 5.5.3.96: Graphical Analysis Use a graphing utility to graph the functions an...
 5.96: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.3.97: In Exercises 97102, determine whether the statement is true or fals...
 5.97: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.3.98: In Exercises 97102, determine whether the statement is true or fals...
 5.98: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.3.99: In Exercises 97102, determine whether the statement is true or fals...
 5.99: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.3.100: In Exercises 97102, determine whether the statement is true or fals...
 5.100: In Exercises 93100, solve the logarithmic equation algebraically. A...
 5.5.3.101: In Exercises 97102, determine whether the statement is true or fals...
 5.101: In Exercises 101104, use a graphing utility to graph and solve the ...
 5.5.3.102: In Exercises 97102, determine whether the statement is true or fals...
 5.102: In Exercises 101104, use a graphing utility to graph and solve the ...
 5.5.3.103: In Exercises 103106, use the changeofbase formula to rewrite the ...
 5.103: In Exercises 101104, use a graphing utility to graph and solve the ...
 5.5.3.104: In Exercises 103106, use the changeofbase formula to rewrite the ...
 5.104: In Exercises 101104, use a graphing utility to graph and solve the ...
 5.5.3.105: In Exercises 103106, use the changeofbase formula to rewrite the ...
 5.105: Compound Interest You deposit $8500 in an account that pays 1.5% in...
 5.5.3.106: In Exercises 103106, use the changeofbase formula to rewrite the ...
 5.106: Meteorology The speed of the wind (in miles per hour) near the cent...
 5.5.3.107: Discussion A classmate claims that the following are true. (a) (b) ...
 5.107: In Exercises 107112, match the function with its graph. [The graphs...
 5.5.3.108: HOW DO YOU SEE IT? The figure shows the graphs of and Match each fu...
 5.108: In Exercises 107112, match the function with its graph. [The graphs...
 5.5.3.109: Think About It For how many integers between 1 and 20 can you appro...
 5.109: In Exercises 107112, match the function with its graph. [The graphs...
 5.110: In Exercises 107112, match the function with its graph. [The graphs...
 5.111: In Exercises 107112, match the function with its graph. [The graphs...
 5.112: In Exercises 107112, match the function with its graph. [The graphs...
 5.113: Finding an Exponential Model Find the exponential model that fits t...
 5.114: Wildlife Population A species of bat is in danger of becoming extin...
 5.115: Test Scores The test scores for a biology test follow a normal dist...
 5.116: Typing Speed In a typing class, the average number of words per min...
 5.117: . Sound Intensity The relationship between the number of decibels a...
 5.118: Graph of an Exponential Function Consider the graph of Describe the...
 5.119: In Exercises 119 and 120, determine whether the equation is true or...
 5.120: In Exercises 119 and 120, determine whether the equation is true or...
Solutions for Chapter 5: Exponential and Logarithmic Functions
Full solutions for College Algebra  9th Edition
ISBN: 9781133963028
Solutions for Chapter 5: Exponential and Logarithmic Functions
Get Full SolutionsCollege Algebra was written by and is associated to the ISBN: 9781133963028. This textbook survival guide was created for the textbook: College Algebra, edition: 9. Since 566 problems in chapter 5: Exponential and Logarithmic Functions have been answered, more than 35909 students have viewed full stepbystep solutions from this chapter. Chapter 5: Exponential and Logarithmic Functions includes 566 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).