342 CHAPTER 5 Exponential and Logarithmic Functions 23. ( ) ( ) + = + − x x log7 6 1 log 1 24. ( ) ( ) − − = x x log 2 log 3 1 25. ( ) ( ) + + + = x x log 7 log 8 1 2 2 26. ( ) ( ) + + + = x x log 4 log 3 1 6 6 27. ( ) ( ) + = − + x x log 6 1 log 4 8 8 28. ( ) ( ) + = − − x x log 3 1 log 1 5 5 29. ( ) + + = x x ln ln 2 4 30. ( ) + − = x x ln 1 ln 2 31. ( ) ( ) + + + = x x log 8 log 7 2 9 9 32. ( ) ( ) + + + = x x log 1 log 7 3 2 2 33. ( ) ( ) + − − =− x x x x log log 1 1 3 2 1 3 2 34. ( ) ( ) − − + = x x log 9 log 3 3 4 2 4 35. ( ) ( ) ( ) ( ) − − + = − − + x x x x log 1 log 6 log 2 log 3 a a a a 36. ( ) ( ) + − = + x x x log log 2 log 4 a a a 37. ( ) − − = x 2 log 3 log8 log2 5 5 5 38. ( ) − = + − x x log 2log5 log 1 2 log 10 3 3 3 3 39. ( ) + = + x 2 log 2 3log 2 log 4 6 6 6 40. ( ) − = x 3log log22log4 7 7 7 41. ( ) ( ) + = + x x 2 log 2 log 4 7 13 13 42. ( ) − = x log 1 1 3 log2 43. ( ) − = x x log 3 log 10 3 2 3 44. − + = x x ln 3 ln 2 0 In Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places. 73. ( ) ( ) + − − = x x log 1 log 2 1 5 4 74. ( ) ( ) − − + = x x log 1 log 2 2 2 6 75. = − e x x 76. = + e x 2 x2 77. = e x x 2 78. = e x x 3 79. = − x x ln 80. ( ) = − + x x ln 2 2 81. = − x x ln 1 3 82. = − x x ln 2 83. + = e x ln 4 x 84. − = e x ln 4 x 85. = −e x ln x 86. = − −e x ln x In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 45. = − 2 8 x 5 46. = −5 25 x 47. = 2 10 x 48. = 3 14 x 49. = −8 1.2 x 50. = −2 1.5 x 51. ( ) = 5 2 8 x3 52. ( ) = 0.3 4 0.2 x 0.2 53. = − 3 4 x x 1 2 54. = + − 2 5 x x 1 1 2 55. ( ) = − 3 5 7 x x 1 56. ( ) = − 4 3 5 x x 1 57. = − 1.2 (0.5) x x 58. = + − 0.3 1.7 x x 1 2 1 59. π = − e x x 1 60. π = + ex x 3 61. + − = 2 2 12 0 x x 2 62. + − = 3 3 2 0 x x 2 63. + − = + 3 3 4 0 x x 2 1 64. + − = + 2 2 12 0 x x 2 2 65. + − = + 16 4 3 0 x x 1 66. − + = + 9 3 1 0 x x 1 67. − ⋅ = − 25 8 5 16 x x 68. − ⋅ = − 36 6 6 9 x x 69. ⋅ + ⋅ + = 3 4 4 2 8 0 x x 70. ⋅ + ⋅ + = 2 49 11 7 5 0 x x 71. − ⋅ = − 4 10 4 3 x x 72. − ⋅ = − 3 14 3 5 x x Applications and Extensions 101. ( ) = + f x x ( ) log 3 2 and ( ) = + g x x ( ) log 3 1 . 2 (a) Solve ( ) = f x 3.What point is on the graph of f ? (b) Solve ( ) = g x 4.What point is on the graph of g? (c) Solve ( ) ( ) = f x g x . Do the graphs of f and g intersect? If so, where? (d) Solve ( )( ) + = f g x 7. (e) Solve ( )( ) − = f g x 2. Mixed Practice In Problems 87–100, solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. 87. ( ) ( ) − = + x x log 7 5 log 1 9 3 88. ( ) + − = x x log 1 log 1 2 4 89. ( ) + − = x x log 3 2 log 3 2 4 90. + + = x x x log log log 7 16 4 2 91. + = x x log 3log 14 9 3 92. ( ) + = x x 2 log 3log log 16 4 2 8 2 93. ( ) = − 2 2 x x 3 2 2 94. = x log 4 x 2 log 2 95. + = − e e 2 1 x x 96. + = − e e 2 3 x x 97. − = − e e 2 2 x x 98. − = − − e e 2 2 x x 99. + = x x log log 1 5 3 100. + = x x log log 3 2 6 [Hint: Change ( ) −x log 7 5 9 to base 3.] [Hint: Multiply each side by ex.] [Hint: Use the Change-of-Base Formula.]
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