Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\log 10^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\ln e^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\ln e^{-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 14, evaluate the expression without using a calculator. \(\log 10^{-3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(\frac{x^{5} y^{-2}}{x^{2} y^{-4}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(\frac{u^{-3} v^{7}}{u^{-2} v^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(\left(x^{6} y^{-2}\right)^{1 / 2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(\left(x^{-8} y^{12}\right)^{3 / 4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(\frac{\left(u^{2} v^{-4}\right)^{1 / 2}}{\left(27 u^{6} v^{-6}\right)^{1 / 3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Exercise numbers with a gray background indicate problems that the authors have designed to be solved without a calculator. In Exercises 510, simplify the expression. \(??\frac{\left(x^{-2} y^{3}\right)^{-2}}{\left(x^{3} y^{-2}\right)^{-3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. ln 8x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. ln 9y

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log \frac{3}{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log \frac{2}{y}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log _{2} y^{5}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log _{2} x^{-2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log x^{3} y^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log x y^{3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\ln \frac{x^{2}}{y^{3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log 1000 x^{4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\log \sqrt[4]{\frac{x}{y}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 112, assuming x and y are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. \(\ln \frac{\sqrt[3]{x}}{\sqrt[3]{y}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. log x + log y

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. log x + log 5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. ln y - ln 3

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. ln x - ln y

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. \(\frac{1}{3} \log x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. \(\frac{1}{5} \log z\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. 2 ln x + 3 ln y

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. 4 log y - log z

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. 4 log (xy) - 3 log (yz)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1322, assuming x, y, and z are positive, use properties of logarithms to write the expression as a single logarithm. \(3 \ln \left(x^{3} y\right)+2 \ln \left(y z^{2}\right)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{2} 7\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{5} 19\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{8} 175\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{12} 259\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{0.5} 12\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2328, use the change-of-base formula and your calculator to evaluate the logarithm. \(\log _{0.2} 29\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the expression using only natural logarithms. \(\log _{3} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the expression using only natural logarithms. \(\log _{7} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the expression using only natural logarithms. \(\log _{2}(a+b)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 2932, write the expression using only natural logarithms. \(\log _{5}(c-d)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. \(\log _{2} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. \(\log _{4} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. \(\log _{1 / 2}(x+y)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. \(\log _{1 / 3}(x-y)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. Prove the quotient rule of logarithms.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3336, write the expression using only common logarithms. Prove the power rule of logarithms.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, describe how to transform the graph of g(x) = ln x into the graph of the given function. Sketch the graph by hand and support it with a grapher. \(f(x)=\log _{4} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, describe how to transform the graph of g(x) = ln x into the graph of the given function. Sketch the graph by hand and support it with a grapher. \(f(x)=\log _{7} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, describe how to transform the graph of g(x) = ln x into the graph of the given function. Sketch the graph by hand and support it with a grapher. \(f(x)=\log _{1 / 3} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 3942, describe how to transform the graph of g(x) = ln x into the graph of the given function. Sketch the graph by hand and support it with a grapher. \(f(x)=\log _{1 / 5} x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4346, match the function with its graph. Identify the window dimensions, Xscl, and Yscl of the graph. \(f(x)=\log _{4}(2-x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4346, match the function with its graph. Identify the window dimensions, Xscl, and Yscl of the graph. \(f(x)=\log _{6}(x-3)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4346, match the function with its graph. Identify the window dimensions, Xscl, and Yscl of the graph. \(f(x)=\log _{0.5}(x-2)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4346, match the function with its graph. Identify the window dimensions, Xscl, and Yscl of the graph. \(f(x) = \mathrm {log}_{0.7} (3 - x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, graph the function, and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. \(f(x) = \mathrm {log}_2 (8x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, graph the function, and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. \(f(x) = \mathrm {log}_{1/3} (9x)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, graph the function, and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. \(f(x) = \mathrm {log} (x^2)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 4750, graph the function, and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. \(f(x) = \mathrm {ln} (x^3)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Sound Intensity Compute the sound intensity level in decibels for each sound listed in Table 3.21.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Earthquake Intensity The Richter scale magnitude R of an earthquake is based on the features of the associated seismic wave and is measured by R=log (a/T)+B, where a is the amplitude in (micrometers), T is the period in seconds, and B accounts f

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Light Intensity in Lake Erie The relationship between intensity I of light (in lumens) at a depth of x feet in Lake Erie is given by \(\mathrm {log} \frac {I}{12}=-0.00235x\). What is the intensity at a depth of 40 ft?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Light Intensity in Lake Superior The relationship between intensity I of light (in lumens) at a depth of x feet in Lake Superior is given by \(\mathrm {log} \frac {I}{12}=-0.0125x\). What is the intensity at a depth of 10 ft?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Use the change-of-base formula to explain how we know that the graph of \(f(x)=\mathrm {log}_3 \ x\) can be obtained by applying a transformation to the graph of g(x) = ln x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Writing to Learn Use the change-of-base formula to explain how the graph of \(f(x)=\mathrm {log}_{0.8} x\) can be obtained by applying transformations to the graph of g(x) = log x.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The logarithm of the product of two positive numbers is the sum of the logarithms of the numbers. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
True or False The logarithm of a positive number is positive. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, solve the problem without using a calculator. Multiple Choice log 12 = (A) 3 log 4 (B) log 3 + log 4 (C) 4 log 3 (D) \(\mathrm {log} \ 3 \cdot \mathrm {log} \ 4\) (E) 2 log 6

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, solve the problem without using a calculator. Multiple Choice \( \mathrm {log}_9 \ 64=\) (A) \(5 \ \mathrm {log}_3 \ 2\) (B) \((\mathrm {log}_3 \ 8)^2\) (C) (ln 64 )/(ln 9) (D) \(2 \ \mathrm {log}_9 \ 32\) (E) (log 64)/9

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, solve the problem without using a calculator. Multiple Choice \(ln \ x^5=\) (A) 5 ln x (B) \(2 \ ln \ x^3\) (C) x ln 5 (D) \(3 \ ln \ x^2\) (E) \(ln \ x^2 \cdot ln \ x^3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5962, solve the problem without using a calculator. Multiple Choice \(log_{1/2}x^2=\) (A) \(-2 \log _2 x\) (B) \(2 \log _2 x\) (C) \(-0.5 \log _2 x\) (D) \(0.5 \log _2 x\) (E) \(-2 \log _2|x|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
(a) Compute the power regression model for the following data. (b) Predict the y-value associated with x=7.1 using the power regression model. (c) Re-express the data in terms of their natural logarithms and make a scatter plot of (ln x, ln

Precalculus: Graphical, Numerical, Algebraic 8th Edition
(a) Compute the power regression model for the following data. (b) Predict the y-value associated with x = 9.2 using the power regression model. (c) Re-express the data in terms of their natural logarithms and make a scatter plot of (ln x,

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Keeping WarmRevisited Recall from Exercise 55 of Section 2.2 that scientists have found the pulse rate r of mammals to be a power function of their body weight w. (a) Re-express the data in Table 3.22 in terms of their common logarithms and m

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Let a = log 2 and b = log 3. Then, for example, log 6 = a + b and log 15 = 1 - a + b. List all of the positive integers less than 100 whose common logs can be written as expressions involving a or b or both. (Hint: See Exploration 1 on page 283.)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Solve \(\ln x>\sqrt[3]{x}\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Solve \(1.2^x \leq \log _{1.2} x\).

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Group Activity Work in groups of three. Have each group member graph and compare the domains for one pair of functions. (a) \(f(x)=2 \ln x+\ln (x-3)\) and \(g(x)=\ln x^2(x-3)\) (b) \(f(x)=\ln (x+5)-\ln (x-5)\) and \(g(x)=\ln \frac{x+5}{x-5}\) (c) \(f(x)=\log (x+3)^2\) and \(g(x)=2 \log (x

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove the change-of-base formula for logarithms.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Prove that f(x) = log x ln x is a constant function with restricted domain by finding the exact value of the constant log x ln x expressed as a common logarithm.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Graph f(x) = ln (ln (x)) , and analyze it for domain, range, continuity, increasing or decreasing behavior, symmetry, asymptotes, end behavior, and invertibility.