474 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 58. Concept Check To graph the function ƒ1x2 = -log51x - 72 - 4, reflect the graph of y = log5 x across the -axis, then shift the graph to the right units and down units. Use the properties of logarithms to rewrite each expression. Simplify the result if possible. Assume all variables represent positive real numbers. See Example 5. 71. log2 6x y 72. log3 4p q 73. log5 527 3 74. log2 223 5 75. log412x + 5y2 76. log617m+ 3q2 77. log2B5r3 z5 78. log3B3 m5n4 t2 79. log2 ab cd 80. log2 xy tqr 81. log3 2x # 23 y w22z 82. log4 23 a # 24 b 2c # 23 d2 Graph each function. Give the domain and range. See Example 4. 59. ƒ1x2 = 1log2 x2 + 3 60. ƒ1x2 = log21x + 32 61. ƒ1x2 = 0 log21x + 32 0 Graph each function. Give the domain and range. See Example 4. 62. ƒ1x2 = 1log1/2 x2 - 2 63. ƒ1x2 = log1/21x - 22 64. ƒ1x2 = 0 log1/21x - 22 0 65. (7, 0) 0 x = –1 (0, –3) (1, –2) x y 66. (7, 1) 0 x = 3 (4, –1) (5, 0) x y 67. (1, –1) 0 x = 3 (2, –2) (–1, 0) x y 68. 0 x = –3 (–2, 0) (–1, –1) (1, –2) x y 69. 0 x = 1 (2, 0) (4, –1) ( , 1) 4 3 x y 70. 0 x = 5 (–3, –3) (3, –1) (4, 0) x y Connecting Graphs with Equations Write an equation for the graph given. Each represents a logarithmic function ƒ with base 2 or 3, translated and/or reflected. See the Note following Example 4. Write each expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers, with a≠1 and b≠1. See Example 6. 83. loga x + loga y - loga m 84. logb k + logb m- logb a 85. loga m- loga n - loga t 86. logb p - logb q - logb r 87. 1 3 logb x 4y5 - 3 4 logb x 2y 88. 1 2 loga p3q4 - 2 3 loga p4q3 89. 2 loga1z + 12 + loga13z + 22 90. 5 loga1z + 72 + loga12z + 92 91. - 2 3 log5 5m2 + 1 2 log5 25m2 92. - 3 4 log3 16p4 - 2 3 log3 8p3
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