520 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 24. Concept Check What is the base of the logarithmic function whose graph contains the point 181, 42? 25. Concept Check What is the base of the exponential function whose graph contains the point A -4, 1 16B? Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers. 26. log5 Ax2y425 m3p B 27. log 3 mn 5r 28. log7 17k + 5r 22 Use a calculator to find an approximation to four decimal places for each logarithm. 29. log 0.0411 30. log 45.6 31. ln 144,000 32. ln 470 33. log2/3 5 8 34. log3 769 Solve each equation. Give solutions in exact form. 53. 3 ln x = 13 54. ln 5x = 16 55. log 12x + 72 = 0.25 56. ln x + ln x3 = 12 57. log2 1x 3 + 52 = 5 58. log 3 1x 2 - 92 = 3 59. log4 313x + 121x - 424 = 2 60. ln eln x - ln 1x - 42 = ln 3 61. log x + log 113 - 3x2 = 1 62. log7 13x + 22 - log7 1x - 22 = 1 63. ln 16x2 - ln 1x + 12 = ln 4 64. log162x + 1 = 1 4 65. ln 3ln e-x4 = ln 3 66. S = a ln a1 + n ab, for n 67. d = 10 log I I0 , for I0 68. D= 200 + 100 log x, for x 69. Use a graphing calculator to solve the equation e x = 4 - ln x. Give solution(s) to the nearest thousandth. A. 5log5 96 B. 5log9 56 C. e log 9 log 5f D. e ln 9 ln 5f Solve each equation. Unless otherwise specified, give irrational solutions as decimals correct to the nearest thousandth. 35. 16x+4 = 83x-2 36. 4x = 12 37. 32x-5 = 13 38. 2x+3 = 5x 39. 6x+3 = 4x 40. e x-1 = 4 41. e2-x = 12 42. 2e5x+2 = 8 43. 10e3x-7 = 5 44. 5x+2 = 22x-1 45. 6x-3 = 34x+1 46. e8x # e2x = e20 47. e6x # e x = e21 48. 10011.022x/4 = 200 49. 2e2x - 5e x - 3 = 0 (Give exact form.) 50. a 1 2b x + 2 = 0 51. 411.062x + 2 = 8 52. Concept Check Which one or more of the following choices is the solution set of 5x = 9?
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