SECTION 5.4 Logarithmic Functions 323 In Problems 41–52, find the domain of each function. 41. ( ) ( ) = − f x x ln 3 42. ( ) ( ) = − g x x ln 1 43. ( ) = F x x log2 2 44. ( ) = H x x log5 3 45. ( ) ( ) = − − f x x 3 2 log 2 5 4 46. ( ) ( ) = + + g x x 8 5 ln 2 3 47. ( ) ( ) = + f x x ln 1 1 48. ( ) ( ) = − g x x ln 1 5 49. ( ) ( ) = + g x x x log 1 5 50. ( ) ( ) = − h x x x log 1 3 51. ( ) = f x x ln 52. ( ) = g x x 1 ln In Problems 53–60, use a calculator to evaluate each expression. Round your answer to three decimal places. 53. ln 5 3 54. ln5 3 55. ln 10 3 0.04 56. − ln 2 3 0.1 57. + + ln4 ln2 log4 log2 58. + + log15 log20 ln15 ln20 59. + − 2 ln5 log50 log4 ln2 60. − + 3log80 ln5 log5 ln20 61. Find a so that the graph of ( ) = f x x loga contains the point ( ) 2, 2 . 62. Find a so that the graph of ( ) = f x x loga contains the point ( ) − 1 2 , 4. In Problems 91–114, solve each equation. 91. = x log 2 3 92. = x log 3 5 93. ( ) + = x log 3 4 5 2 94. ( ) − = x log 3 2 2 3 95. = log 16 2 x 96. ( ) = log 1 8 3 x 97. = e ln 5 x 98. = −e ln 8 x2 99. = x log 64 4 100. = x log 625 5 101. = +x log 243 2 1 3 102. = +x log 36 5 3 6 In Problems 63–66, graph each function and its inverse on the same set of axes 63. ( ) ( ) = = − f x f x x 3 ; log x 1 3 64. ( ) ( ) = = − f x f x x 4 ; log x 1 4 65. ( ) ( ) ( ) = = − f x f x x 1 2 ; log x 1 1 2 66. ( ) ( ) ( ) = = − f x f x x 1 3 ; log x 1 1 3 In Problems 75–90, use the given function f. (a) Find the domain of f. (b) Graph f. (c) From the graph, determine the range and any asymptotes of f. (d) Find −f 1, the inverse of f. (e) Find the domain and the range of −f .1 (f) Graph −f .1 75. ( ) ( ) = + f x x ln 4 76. ( ) ( ) = − f x x ln 3 77. ( ) = + f x x 2 ln 78. ( ) ( ) = − − f x x ln 79. ( ) ( ) = − f x x ln 2 3 80. ( ) ( ) = − + f x x 2 ln 1 81. ( ) ( ) = − + f x x log 4 2 82. ( ) = − f x x 1 2 log 5 83. ( ) ( ) = f x x 1 2 log 2 84. ( ) ( ) = − f x x log 2 85. ( ) ( ) = + + f x x 3 log 2 3 86. ( ) ( ) = − + f x x 2 log 1 3 87. ( ) = − + f x e 3 x 2 88. ( ) = + f x e3 2 x 89. ( ) = + f x 2 4 x 3 90. ( ) = − + f x 3x 1 In Problems 67–74, the graph of a logarithmic function is given. Match each graph to one of the following functions: (A) = y x log3 (B) ( ) = − y x log3 (C) = − y x log3 (D) ( ) = − − y x log3 (E) = − y x log 1 3 (F) ( ) = − y x log 1 3 (G) ( ) = − y x log 1 3 (H) = − y x 1 log3 67. x y 25 1 3 23 x 5 0 68. x5 3 21 23 x 5 1 69. x y 1 3 25 23 x 5 0 70. x y 5 3 21 23 x 5 0 71. x 5 3 21 23 x 5 0 72. y x 5 3 21 23 x 5 0 73. x y 5 3 21 23 x 5 0 74. x y 1 3 25 23 x 5 1
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