497 4.5 Exponential and Logarithmic Equations 20. 3x-4 = 72x+5 21. ex2 = 100 22. ex4 = 1000 23. e3x-7 # e-2x = 4e 24. e1-3x # e5x = 2e 25. a 1 3b x = -3 26. a 1 9b x = -9 27. 0.0511.152x = 5 28. 1.210.92x = 0.6 29. 3122x-2 + 1 = 100 30. 511.223x-2 + 1 = 7 31. 211.052x + 3 = 10 32. 311.42x - 4 = 60 33. 511.0152x-1980 = 8 34. 611.0242x-1900 = 9 35. e2x - 6ex + 8 = 0 36. e2x - 8ex + 15 = 0 37. 2e2x + ex = 6 38. 3e2x + 2ex = 1 39. 52x + 315x2 = 28 40. 32x - 1213x2 = -35 Solve each equation. Give solutions in exact form. See Examples 5–9. 41. 5 lnx = 10 42. 3 lnx = 9 43. ln4x = 1.5 44. ln2x = 5 45. log12 - x2 = 0.5 46. log13 - x2 = 0.75 47. log612x + 42 = 2 48. log518 - 3x2 = 3 49. log41x 3 + 372 = 3 50. log 71x 3 + 652 = 0 51. lnx + lnx2 = 3 52. logx + logx2 = 3 53. log331x + 521x - 324 = 2 54. log4313x + 821x - 624 = 3 55. log2312x + 821x + 424 = 5 56. log5313x + 521x + 124 = 1 57. logx + log1x + 152 = 2 58. logx + log12x + 12 = 1 59. log1x + 252 = log1x + 102 + log4 60. log13x + 52 - log12x + 42 = 0 61. log1x - 102 - log1x - 62 = log2 62. log1x2 - 92 - log1x - 32 = log5 63. ln17 - x2 + ln11 - x2 = ln125 - x2 64. ln13 - x2 + ln15 - x2 = ln150 - 6x2 65. log81x + 22 + log81x + 42 = log8 8 66. log215x - 62 - log21x + 12 = log2 3 67. log21x 2 - 1002 - log 21x + 102 = 1 68. log21x - 22 + log21x - 12 = 1 69. logx + log1x - 212 = log100 70. logx + log13x - 132 = log10 71. log19x + 52 = 3 + log1x + 22 72. log111x + 92 = 3 + log1x + 32 73. ln14x - 22 - ln4 = -ln1x - 22 74. ln15 + 4x2 - ln13 + x2 = ln3 75. log51x + 22 + log51x - 22 = 1 76. log21x - 72 + log2 x = 3 77. log212x - 32 + log21x + 12 = 1 78. log513x + 22 + log51x - 12 = 1 79. lnex - 2 lne = lne4 80. lnex - lne3 = lne3 81. log21log2 x2 = 1 82. logx = 2logx 83. logx2 = 1logx22 84. log 222x 2 = 3 2 85. Concept Check Consider the following statement: “We must reject any negative proposed solution when we solve an equation involving logarithms.” Is this correct? Why or why not? 86. Concept Check What values of x could not possibly be solutions of the following equation? loga14x - 72 + loga1x 2 + 42 = 0
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