Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
79.
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EBK COLLEGE ALGEBRA ESSENTIALS
- In Exercises 16–18, write each equation in its equivalent logarithmic form. 16. 6 = 216 17. b' = 625 18. 13' = 874arrow_forwardIn Exercises 128–131, graph f and g in the same viewing rectangle. Then describe the relationship of the graph of g to the graph of f. 128. f(x) = In x, g(x) = In(x + 3) 129. f(x) = In x, g(x) = In x + 3 130. f(x) = log x, g(x) = -log x 131. (x) = log x, g(x) = log(x – 2) + 1arrow_forwardFor Exercises 13–18, use the quotient property of logarithms to write the logarithm as a difference of logarithms. Then simplify if possible. (See Example 2) 13. logiz 14. log 15. In 1000 16. In 17. log 18. log 100arrow_forward
- In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 64. 24x-2 = 64 65. 125* = 25 %3D 66. 10 = 7000 67. 9*+2 = 27- 68. 8* = 12,143 69. 9esx = 1269 %3D 70. e12-5x - 7 = 123 71. 54r+2 = 37,500 %3D 72. 3*+4 = 72r-1 73. e2 - e - 6 = 0arrow_forwardFor Exercises 33–38, find the exact value of each expression without the use of a calculator. (See Example 5)arrow_forwardIn Exercises 41–67, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 41. log5 + log2 57. 3ln x - 1/3ln y 67. 1/3 [2ln(x+5)-ln x-ln(x2 -4)]arrow_forward
- Your cardiac index is your heart's output, in liters of blood per minute, divided by your body's surface area, in square meters. The cardiac index, C(x), can be modeled by 7.644 C(x) = 10 s xs 80, where x is an individual's age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96. 7.644 C(x) = %3D 10 20 30 40 50 60 70 80 90 Age 95. a. Find the cardiac index of a 32-year-old. Express the denominator in simplified radical form and reduce the fraction. b. Use the form of the answer in part (a) and a calculator to express the cardiac index to the nearest hundredth. Identify your solution as a point on the graph. 96. a. Find the cardiac index of an 80-year-old. Express the denominator in simplified radical form and reduce the fraction. Cardiac Index liters per minute squar e met ers 654 32arrow_forwardIn Exercises 1–6, solve for x.arrow_forwardAmerica is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?arrow_forward
- 7) Solve for "x" in the equation log,(x + 2) -1 = 4 (3 decimal point accuracy). Page Q + 1 & 6 7 8 toarrow_forwardAn exponential function,f (x), passes through the points(2, 5)and (8, 20). Determine the value of f(25) to the nearest integer.arrow_forwardWrite an exponential function in the form abº that goes through points (0, 4) and (5, 128).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage