131 and 132 use the following discussion: The Richter

Solve each inequality: (a) 3x - 7 8 - 2x (pp. A76A77) (b) x2 - x - 6 7 0 (pp. 168171)

Solve the inequality: x - 1 x + 4 7 0 (pp. 238240)

Solve: 2x + 3 = 9 (pp. A43A45)

The domain of the logarithmic function f1x2 = loga x is

The graph of every logarithmic function f1x2 = loga x, where a 7 0, and a 1, passes through three points: , , and .

If the graph of a logarithmic function f1x2 = loga x, where a 7 0 and a 1, is increasing, then its base must be larger than .

If the graph of a logarithmic function f1x2 = loga x, where a 7 0 and a 1, is increasing, then its base must be larger than .

The graph of f1x2 = loga x, where a 7 0 and a 1, has an x-intercept equal to 1 and no y-intercept. C

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 916, change each exponential statement to an equivalent statement involving a logarithm.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 1724, change each logarithmic statement to an equivalent statement involving an exponent.

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 2536, find the exact value of each logarithm without using a calculator

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 37 48, find the domain of each function.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

In Problems 49 56, use a calculator to evaluate each expression. Round your answer to three decimal places.

Find a so that the graph of f1x2 = loga x contains the point (2, 2).

Find a so that the graph of f1x2 = loga x contains the point a 1 2 , -4b.

In Problems 59 62, graph each function and its inverse on the same Cartesian plane.

In Problems 59 62, graph each function and its inverse on the same Cartesian plane.

In Problems 59 62, graph each function and its inverse on the same Cartesian plane.

In Problems 59 62, graph each function and its inverse on the same Cartesian plane.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 6370, the graph of a logarithmic function is given. Match each graph to one of the following functions.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 71 86, use the given function f to: (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find f -1, the inverse of f. (e) Find the domain and the range of f -1. (f) Graph f -1.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

In Problems 87110, solve each equation.

Suppose that G(x) = log3(2x + 1) - 2. (a) What is the domain of G? (b) What is G(40)? What point is on the graph of G? (c) If G1x2 = 3,what is x? What point is on the graph of G? (d) What is the zero of G?

Suppose that F(x) = log2(x + 1) - 3. (a) What is the domain of F ? (b) What is F(7)? What point is on the graph of F ? (c) If F(x) = -1, what is x? What point is on the graph of F ? (d) What is the zero of F ?

In Problems 113116, graph each function. Based on the graph, state the domain and the range and find any intercepts

In Problems 113116, graph each function. Based on the graph, state the domain and the range and find any intercepts

In Problems 113116, graph each function. Based on the graph, state the domain and the range and find any intercepts

In Problems 113116, graph each function. Based on the graph, state the domain and the range and find any intercepts

The pH of a chemical solution is given by the formula pH = -log10[H+] where [H+] is the concentration of hydrogen ions in moles per liter. Values of pH range from 0 (acidic) to 14 (alkaline). (a) What is the pH of a solution for which [H+] is 0.1? (b) What is the pH of a solution for which [H+] is 0.01? (c) What is the pH of a solution for which [H+] is 0.001? (d) What happens to pH as the hydrogen ion concentration decreases? (e) Determine the hydrogen ion concentration of an orange (pH = 3.5). (f) Determine the hydrogen ion concentration of human blood (pH = 7.4).

is a measure of the diversity of a population. The diversity index is given by the formula H = - 1p1 log p1 + p2 log p2 +p+ pn log pn2 where p1 is the proportion of the population that is species 1, p2 is the proportion of the population that is species 2, and so on. (a) According to the U.S. Census Bureau, the distribution of race in the United States in 2009 was as follows: Compute the diversity index of the United States in 2009. (b) The largest value of the diversity index is given by Hmax = log(S), where S is the number of categories of race. Compute Hmax. (c) The evenness ratio is given by EH = H Hmax , where 0 EH 1. If EH = 1, there is complete evenness. Compute the evenness ratio for the United States.

The atmospheric pressure p on an object decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the function p1h2 = 760e-0.145h (a) Find the height of an aircraft if the atmospheric pressure is 320 millimeters of mercury. (b) Find the height of a mountain if the atmospheric pressure is 667 millimeters of mercury.

The normal healing of wounds can be modeled by an exponential function. If A0 represents the original area of the wound and if A equals the area of the wound, then the function A(n) = A0 e-0.35n describes the area of a wound after n days following an injury when no infection is present to retard the healing. Suppose that a wound initially had an area of 100 square millimeters. (a) If healing is taking place, after how many days will the wound be one-half its original size? (b) How long before the wound is 10% of its original size?

Between 12:00 pm and 1:00 pm, cars arrive at Citibanks drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 pm. F(t) = 1 - e-0.1t (a) Determine how many minutes are needed for the probability to reach 50%. (b) Determine how many minutes are needed for the probability to reach 80%. (c) Is it possible for the probability to equal 100%? Explain.

Between 5:00 pm and 6:00 pm, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 5:00 pm. F(t) = 1 - e-0.15t (a) Determine how many minutes are needed for the probability to reach 50%. (b) Determine how many minutes are needed for the probability to reach 80%.

The formula D = 5e-0.4h can be used to find the number of milligrams D of a certain drug that is in a patients bloodstream h hours after the drug was administered. When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?

A model for the number N of people in a college community who have heard a certain rumor is N = P(1 - e-0.15d ) where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many days will elapse before 450 students have heard the rumor?

The equation governing the amount of current I (in amperes) after time t (in seconds) in a simple RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in volts) is I = E R 31 - e-(R>L)t 4 If E = 12 volts, R = 10 ohms, and L = 5 henrys, how long does it take to obtain a current of 0.5 ampere? Of 1.0 ampere? Graph the equation.

Psychologists sometimes use the function L(t) = A(1 - e-kt) to measure the amount L learned at time t. The number A represents the amount to be learned, and the number k measures the rate of learning. Suppose that a student has an amount A of 200 vocabulary words to learn. A psychologist determines that the student learned 20 vocabulary words after 5 minutes. (a) Determine the rate of learning k. (b) Approximately how many words will the student have learned after 10 minutes? (c) After 15 minutes? (d) How long does it take for the student to learn 180 words?

Problems 127130 use the following discussion: The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x I0 , where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds

Problems 127130 use the following discussion: The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x I0 , where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds

Problems 127130 use the following discussion: The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x I0 , where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds

Problems 127130 use the following discussion: The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x I0 , where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect. Determine the loudness, in decibels, of each of the following sounds

Problems 131 and 132 use the following discussion: The Richter scale is one way of converting seismographic readings into numbers that provide an easy reference for measuring the magnitude M of an earthquake. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures x millimeters has magnitude M(x), given by M(x) = log x x0 where x0 = 10-3 is the reading of a zero-level earthquake the same distance from its epicenter. In Problems 131 and 132, determine the magnitude of each earthquake

Problems 131 and 132 use the following discussion: The Richter scale is one way of converting seismographic readings into numbers that provide an easy reference for measuring the magnitude M of an earthquake. All earthquakes are compared to a zero-level earthquake whose seismographic reading measures 0.001 millimeter at a distance of 100 kilometers from the epicenter. An earthquake whose seismographic reading measures x millimeters has magnitude M(x), given by M(x) = log x x0 where x0 = 10-3 is the reading of a zero-level earthquake the same distance from its epicenter. In Problems 131 and 132, determine the magnitude of each earthquake

The concentration of alcohol in a persons bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form R = ekx where x is the percent of concentration of alcohol in the bloodstream and k is a constant.

Is there any function of the form y = xa, 0 6 a 6 1, that increases more slowly than a logarithmic function whose base is greater than 1? Explain

In the definition of the logarithmic function, the base a is not allowed to equal 1. Why?

In buying a new car, one consideration might be how well the price of the car holds up over time. Different makes of cars have different depreciation rates. One way to compute a depreciation rate for a car is given here. Suppose that the current prices of a certain automobile are as shown in the table.