A-26 Answers to Selected Exercises 4.3 Exercises 1. (a) C (b) A (c) E (d) B (e) F (f) D 3. 23 = 8 5. E4 9F 7. y x 0 1 5 1 –2 –2 4 f(x) = log 5 x 10, ∞2; 1-∞, ∞2 9. log10 2 + log10 x - log10 7 11. log3 81 = 4 13. log2/3 27 8 = -3 15. 62 = 36 17. A 23 B 8 = 81 19. 5-46 21. E1 2F 23. E 1 4F 25. 586 27. 596 29. E1 5F 31. 5646 33. E 2 3F 35. 52436 37. 5136 39. 536 41. 556 43. E 45. B 47. F 49. x y 2 5 25 –2 f(x) = log5 x 0 51. y x 0 2 4 2 –3 –2 4 f(x) = log5 (x+1) x = –1 53. x y 0 –2 2 –4 f(x) = log1/2(1 – x) x = 1 55. x y 0 3 3 f(x) = log3 (x – 1) + 2 x = 1 57. y x 2 5 –4 –2 2 x = –3 f(x) = log1/2 (x+3) – 2 0 59. y x 0 2 4 6 8 2 4 6 f(x) = (log2x) + 3 10, ∞2; 1-∞, ∞2 63. ƒ1x2 = 3x - 2 65. ƒ1x2 = 2x+3 - 1 67. ƒ1x2 = -2x+2 + 3 69. ƒ1x2 = 3-x + 1 71. E1 2F 73. 5-26 75. 506 77. E 1 2F 79. E1 5F 81. 5-76 83. 5{86 85. 546 87. 5{26 89. 5-276 91. E - 2 3F 93. E 4 3F 95. 536 97. (a) $11,643.88; $2737.34 (b) $11,667.25; $2760.71 99. $22,902.04 101. $3528.81 103. 2.5% 105. Bank A (even though it has the greatest stated rate) 107. (a) 0 −1000 1200 11,000 (b) exponential (c) P(x) = 1013e−0.0001341x 0 −1000 1200 11,000 (d) P115002 ≈828 mb; P111,0002 ≈232 mb 109. (a) 63,000 (b) 42,000 (c) 21,000 111. 50.96 113. 5-0.5, 1.36 115. The variable is located in the base of a power function and in the exponent of an exponential function. 117. ƒ1x2 = 2x 119. ƒ1x2 = A1 4B x 121. ƒ1t2 = 27 # 9t 123. ƒ1t2 = A1 3B 9t 125. 2.717 (A calculator gives 2.718.) 127. yes; an inverse function 55. y x 3 9 3 –2 0 f(x) = ( )–x + 1 1 3 1-∞, ∞2; 10, ∞2 57. y x 3 9 0 3 f(x) = ( ) –x 1 3 1-∞, ∞2; 10, ∞2 59. x y 1 3 0 f(x) = x – 2 + 2 y = 2 ( )1 3 1-∞, ∞2; 12, ∞2 61. x y 2 4 0 f(x) = x + 2 – 1 y = –1 ( )1 3 1-∞, ∞2; 1-1, ∞2 128. x y (0, 1) (1, 0) y = f(x) y = x y = f –1(x) 0 129. x = ay 130. x = 10y 131. x = ey 132. 1q, p2 61. y x 0 f(x) = zlog2(x + 3)z x = –3 4 2 –2 1-3, ∞2; 30, ∞2 63. x y 0 –2 2 3 6 9 f(x) = log1/2(x – 2) x = 2 12, ∞2; 1-∞, ∞2 65. ƒ1x2 = log21x + 12 - 3 67. ƒ1x2 = log21-x + 32 - 2 69. ƒ1x2 = -log31x - 12 71. log2 6 + log2 x - log2 y 73. 1 + 1 2 log5 7 - log5 3 75. This cannot be simplified. 77. 1 2 1log2 5 + 3 log2 r - 5 log2 z2 79. log2 a + log2 b - log2 c - log2 d 81. 1 2 log3 x + 1 3 log3 y - 2 log3 w - 1 2 log3 z 83. loga xy m 85. loga m nt 87. logb1x-1/6y11/122 89. loga31z + 12213z + 224 91. log 5 51/3 m1/3 , or log53 3 5 m 93. 0.7781 95. 0.1761 97. 0.3522 99. 0.7386
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