2 2 log 5 5 log 5 5 2 log 5 25 log 5 75 log 5 3 log 5 75 3 38 3 1 2 1 5 2 1 1 2

2 2 log 5 5 log 5 5 2 log 5 25 log 5 75 log 5 3 log 5

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2 2 log 5 5 log 5 5 2 log 5 25 log 5 75 log 5 3 log 5 75 3 38. 3 1 2 1 5 2 1 1 2 log 4 4 5 2 log 4 4 log 4 2 log 4 32 log 4 4 1 2 log 4 4 5 2 39. log 4 5 x log 4 5 log 4 x 40. log 3 10 z log 3 10 log 3 z 41. log 8 x 4 4 log 8 x 42. log y 2 log y log 2 43. 1 log 5 x log 5 5 x log 5 5 log 5 x 44. log 6 z 3 3 log 6 z 45. ln z ln z 1 2 1 2 ln z 49. ln z 2 ln z 1 , z > 1 ln z z 1 2 ln z ln z 1 2 50. ln x 1 ln x 1 3 ln x ln x 1 x 1 ln x 3 ln x 2 1 x 3 ln x 2 1 ln x 3 46. ln 3 t ln t 1 3 1 3 ln t 47. ln x ln y 2 ln z ln xyz 2 ln x ln y ln z 2 48. log 4 2 log x log y log 4 x 2 y log 4 log x 2 log y 51. 1 2 log 2 a 1 2 log 2 3, a > 1 1 2 log 2 a 1 log 2 3 2 log 2 a 1 9 log 2 a 1 log 2 9 52. ln 6 1 2 ln x 2 1 ln 6 ln x 2 1 1 2 ln 6 x 2 1 ln 6 ln x 2 1
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480 Chapter 5 Exponential and Logarithmic Functions 55. 4 ln x 1 2 ln y 5 ln z ln x 4 ln y ln z 5 ln x 4 y z 5 ln x 4 y ln z 5 56. 1 2 log 2 x 4 log 2 y 4 log 2 z log 2 x log 2 y 4 log 2 z 4 log 2 x y 4 z 4 log 2 x y 4 log 2 z 4 53. 1 3 ln x 1 3 ln y 1 3 ln x ln y ln 3 x y 1 3 ln x y 54. ln x 3 2 ln y 1 2 2 ln x 3 ln y 1 2 ln x 2 ln y 3 ln x 2 y 3 ln x 2 y 3 1 2 1 2 ln x 2 y 3 57. 2 log 5 x 2 log 5 y 3 log 5 z log 5 x 2 log 5 y 2 log 5 z 3 log 5 x 2 y 2 z 3 log 5 x 2 log 5 y 2 z 3 58. log x 4 log y 5 log z log x log y 4 log z 5 log xy 4 z 5 log xy 4 log z 5 59. 3 4 ln x 1 4 ln x 2 3 1 4 3 ln x ln x 2 3 1 4 ln x 3 ln x 2 3 ln 4 x 3 x 2 3 1 4 ln x 3 x 2 3 60. ln x 1 2 ln x 2 ln x ln x 2 1 2 ln x x 2 1 2 ln x 2 x 2 ln x 2 x 2 1 2 61. ln x ln 3 ln 3 x 62. ln y ln t ln yt ln ty 63. log 4 z log 4 y log 4 z y 64. log 5 8 log 5 t log 5 8 t 65. 2 log 2 x 4 log 2 x 4 2 66. 2 3 log 7 z 2 log 7 z 2 2 3 67. 1 4 log 3 5 x log 3 5 x 1 4 log 3 4 5 x 68. 4 log 6 2 x log 6 2 x 4 log 6 1 16 x 4 69. ln x x 1 3 ln x 3 ln x 1 ln x ln x 1 3 70. ln 64 z 4 5 ln 64 ln z 4 5 2 ln 8 5 ln z 4 ln 8 2 ln z 4 5 71. log xz 3 y 2 log x y 2 log z 3 log x 2 log y 3 log z log x log y 2 log z 3 72. log 3 x 3 y 4 z 4 log 3 x 3 y 4 log 3 z 4 3 log 3 x 4 log 3 y 4 log 3 z log 3 x 3 log 3 y 4 log 3 z 4
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Section 5.3 Properties of Logarithms 481 73. ln x x 2 4 4 ln x ln x 2 4 4 ln x 4 ln x 2 4 ln x 4 ln x 2 ln x 2 ln x 4 ln x 2 x 2 74. ln z 4 z 5 4 z 5 2 ln z z 5 4 ln z 5 2 4 ln z ln z 5 2 ln z 5 4 ln z z 5 ln z 5 2 75. ln 3 x x 3 2 x 2 1 1 3 ln x x 3 2 x 2 1 1 3 ln x x 3 2 ln x 2 1 1 3 2 ln x 3 ln x ln x 2 1 1 3 ln x 3 2 ln x ln x 2 1 76. ln x 3 x 2 1 2 2 ln x 3 x 2 1 2 ln x 3 ln x 1 x 1 2 ln x 3 ln x 1 ln x 1 2 3 ln x ln x 1 ln x 1 2 ln x 3 ln x 1 ln x 1 77. log 8 3 y y 4 2 y 1 log 8 3 y y 4 2 log 8 y 1 1 3 log 8 y y 4 2 log 8 y 1 1 3 log 8 y 2 log 8 y 4 log 8 y 1 1 3 log 8 y log 8 y 4 2 log 8 y 1 78. log 4 x 6 x 1 x 1 log 4 x 1 x 1 log 4 x 6 1 2 log 4 x 1 x 1 2 log 4 x 6 1 2 log 4 x 1 2 log 4 x 1 6 log 4 x 1 2 log 4 x 1 log 4 x 1 2 log 4 x 6 79. The second and third expressions are equal by Property 2.
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  • Fall '14
  • Natural logarithm, Logarithm, Inverse Property

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