Problem 1QC: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible... Problem 2QC Problem 3QC Problem 4QC Problem 5QC Problem 6QC Problem 1E: For b 0, what are the domain and range of f(x) = bx? Problem 2E Problem 3E Problem 4E: Sketch a graph of a function that is one-to-one on the intervals (, 2], and [2, ) but is not... Problem 5E Problem 6E Problem 7E Problem 8E Problem 9E: Find the inverse of the function f(x) = 2x. Verify that f(f1(x)=x) and f1(f(x))=x. Problem 10E: Find the inverse of the function f(x)=x, for x 0. Verify that f(f1(x))=x and f1(f(x))=x. Problem 11E: Graphs of inverses Sketch the graph of the inverse function. 39. Problem 12E: Graphs of inverses Sketch the graph of the inverse function. 40. Problem 13E Problem 14E Problem 15E: Explain the meaning of logbx. Problem 16E: How is the property bx+ y = bxby related to the property logb (xy) = logb x + logb y? Problem 17E Problem 18E: Express 25 using base e. Problem 19E Problem 20E: For a certain constant a 1, ln a 3.8067. Find approximate values of log2a and loga2 using the fact... Problem 21E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 22E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 23E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 24E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 25E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 26E: Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible... Problem 27E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 28E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 29E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 30E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 31E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 32E: Graphing inverse functions Find the inverse function (on the given interval, if specified) and graph... Problem 33E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 34E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 35E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 36E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 37E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 38E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 39E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 40E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 41E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 42E: Finding inverse functions Find the inverse f1(x) of each function (on the given interval, if... Problem 43E: Splitting up curves The unit circle x2 + y2 = 1 consists of four one-to-one functions, f1(x), f2(x),... Problem 44E: Splitting up curves The equation y4 = 4x2 is associated with four one-to-one functions f1(x), f2(x),... Problem 45E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 46E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 47E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 48E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 49E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 50E: Properties of logarithms Assume logb x = 0.36, logb y = 0.56, and logb z = 0.83. Evaluate the... Problem 51E: Solving logarithmic equations Solve the following equations. 41. log10 x = 3 Problem 52E: Solving logarithmic equations Solve the following equations. 42. log5 x = 1 Problem 53E: Solving logarithmic equations Solve the following equations. 43. loggx=13 Problem 54E: Solving logarithmic equations Solve the following equations. 44. logb 125 = 3 Problem 55E: Solving logarithmic equations Solve the following equations. 45. ln x = 1 Problem 56E: Solving logarithmic equations Solve the following equations. 46. ln y = 3 Problem 57E: Solving equations Solve the following equations. 53. 7x = 21 Problem 58E: Solving equations Solve the following equations. 54. 2x = 55 Problem 59E: Solving equations Solve the following equations. 55. 33x4 = 15 Problem 60E: Solving equations Solve the following equations. 56. 53x = 29 Problem 61E: Using inverse relations One hundred grams of a particular radioactive substance decays according to... Problem 62E: Mass of juvenile desert tortoises In a study conducted at the University of New Mexico, it was found... Problem 63E: Investment Problems An investment of P dollars is deposited in a savings account that is compounded... Problem 64E: Investment Problems An investment of P dollars is deposited in a savings account that is compounded... Problem 65E: Height and time The height in feet of a baseball hit straight up from the ground with an initial... Problem 66E: Velocity of a skydiver The velocity of a skydiver (in m/s) t seconds after jumping from a plane is... Problem 67E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 68E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 69E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 70E: Calculator base change Write the following logarithms in terms of the natural logarithm. Then use a... Problem 71E: Changing bases Convert the following expressions to the indicated base. 63. 2x using base e Problem 72E: Changing bases Convert the following expressions to the indicated base. 64. 3sin x using base e Problem 73E: Changing bases Convert the following expressions to the indicated base. 65. In |x| using base 5 Problem 74E: Changing bases Convert the following expressions to the indicated base. 66. log2 (x2 + 1) using base... Problem 75E: Changing bases Convert the following expressions to the indicated base. 67. a1/ln a using base e,... Problem 76E: Changing bases Convert the following expressions to the indicated base. 68. a1/log10a using base 10,... Problem 77E: Explain why or why not Determine whether the following statements are true and give an explanation... Problem 78E: Graphs of exponential functions The following figure shows the graphs of y = 2x, y = 3x, y = 2x, and... Problem 79E: Graphs of logarithmic functions The following figure shows the graphs of y = log2 x, y = log4 x, and... Problem 80E: Graphs of modified exponential functions Without using a graphing utility, sketch the graph of y =... Problem 81E: Graphs of modified logarithmic functions Without using a graphing utility, sketch the graph of y =... Problem 82E: Population model A culture of bacteria has a population of 150 cells when it is first observed. The... Problem 83E: Charging a capacitor A capacitor is a device that stores electrical charge. The charge on a... Problem 84E: Large intersection point Use any means to approximate the intersection point(s) of the graphs of... Problem 85E: Finding all inverses Find all the inverses associated with the following functions, and state their... Problem 86E: Finding all inverses Find all the inverses associated with the following functions, and state their... Problem 87E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 88E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 89E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 90E: Finding all inverses Find all the inverses associated with the following functions and state their... Problem 91E: Reciprocal bases Assume that b 0 and b 1. Show that log1/b x = logb x. Problem 92E: Proof of rule L1 Use the following steps to prove that logb xy = logb x + logb y. a. Let x = bp and... Problem 93E Problem 94E: Proof of rule L3 Use the following steps to prove that logb xz = z logb x. a. Let x = bp. Solve this... Problem 95E Problem 96E Problem 97E: Nice property Prove that (logb c)(logc b) = 1, for b 0. c 0, b 1, and c 1. format_list_bulleted