AN40 Answers: Chapter 5 117. y 5 x 5 x 5 0 (21, 0) (1, 0) Domain: x x 0 { } ≠ Range: , ( ) −∞ ∞ Intercepts: 1, 0 , 1, 0 ( ) ( ) − 119. x 5 0 y x 2.5 (1, 0) 5 Domain: x x 0 { } > Range: y y 0 { } ≥ Intercept: 1, 0 ( ) 121. (a) 1 (b) 2 (c) 3 (d) It increases. (e) 0.000316 (f) 3.981 10 8 × − 123. (a) 5.97 km (b) 0.90 km 125. (a) 6.93 min (b) 16.09 min 127. h 2.29, ≈ so the time between injections is about 2 h, 17 min. 129. 0.2695 sec 0.8959 sec y x 2.0 1.6 1.2 0.8 0.4 2.0 0 0.4 1.2 Amperes Seconds (0.8959, 1) (0.2695, 0.5) 131. 50 dB 133. 90 dB 135. 8.1 137. (a) k 11.216 ≈ (b) 6.73 (c) 0.41% (d) 0.14% 139. 64 { } 141. 1, 5 { } − 143. Because y x log1 = means x 1 1 , y = = which cannot be true for x 1 ≠ 145. Zeros: 3, 1 2 , 1 2 , 3; − − x-intercepts: 3, 1 2 , 1 2 , 3 − − 146. 12 147. f f 1 5; 2 17 ( ) ( ) = − = 148. i f x x x x x a 3 ; 7 14 2 20; 1 4 3 2 ( ) + = − + + − = 149. 7 57 4 , 7 57 4 { } − + 150. x y 5 8 8 + = 151. 31, 14 { } − 152. 151.1 cm 153. x x2 4 2 + + 154. x x x 5 3 11 23 3 6 ( ) ( ) ( ) + − + 5.5 Assess Your Understanding (page 333) 1. 0 2. M 3. r 4. M N log log a a + 5. M N log log a a − 6. r M loga 7. 7 8. F 9. F 10. F 11. b 12. b 13. 29 15. 4− 17. 13 19. 1 21. 1 23. 3 25. 6 5 27. 4 29. a b + 31. b a − 33. a3 35. a b 1 5 ( ) + 37. x 2 log6 + 39. y 6 log5 41. x 1 ln + 43. x x ln − 45. u v 2 log 3log a a + 47. ( ) + − x x 2 ln 1 2 ln 1 49. x x 3log log 3 2 2( ) − − 51. x x x log log 2 2 log 3 ( ) ( ) + + − + 53. x x x 1 3 ln 2 1 3 ln 1 2 3 ln 4 ( ) ( ) ( ) − + + − + 55. ( ) ( ) + + + − − x x x ln5 ln 1 2 ln 1 3 3 ln 4 57. u v log5 3 4 59. x log 1 3 5 2 ( ) 61. x x log 1 1 4 4 ( ) − + ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 63. x 2 ln 1 ( ) − − 65. x x log 3 2 2 4 [ ] ( ) − 67. x x log 25 2 3 a 6 ( ) + 69. x x x log 1 3 1 2 2 ( ) ( )( ) + + − ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 71. 2.771 73. 3.880 − 75. 5.615 77. 0.874 79. y x log log 4 = 3 21 23 4 81. y x log 2 log 2 ( ) = + 3 22 22 5 83. y x x log 1 log 1 ( ) ( ) = + − 5 0 4 24 101. x x x x x x x x x x log 1 log 1 log 1 1 log 1 log 1 0 a a a a a 2 2 2 2 2 2 ( ) ( ) ( )( ) ( ) [ ] + − + − − = ⎡ ⎣ + − − − ⎤⎦ = − − = = 103. e e e e e x e ln 1 ln 1 ln ln 1 2 ln 1 x x x x x x 2 2 2 2 2 2 ( ) ( ) [ ] ( ) ( ) + = + = + + = + + − − − 105. y f x x a x a a x log ; implies 1 , a y y y ( ) ( ) = = = = = − so y x f x log . a 1 ( ) − = = − 107. f x x f x x x f x log ; 1 log 1 log 1 log a a a a ( ) ( ) ( ) = = = − = − 109. M N M N M N M N log log log log log log . a a a a a a 1 1 ( ) = ⋅ = + = − − − 111. b b a a log log log 1 log a b b b = = 113. = = = b b a m b n m n b log log log log log a m a m a n a a n 119. 1.78, 1.29, 3.49 { } − 120. A repeated real solution (double root) 121. 2, 1 5 , 5 21 2 , 5 21 2 − − − − + 122. y 10 −10 x 10 −10 Domain: x x 2 or , 2 { } ( ] ≤ −∞ Range: y y 0 or 0, { } [ ) ≥ ∞ 123. , 3 5 (−∞ ⎤ ⎦ ⎥ 124. { } − < < x x 9 7 or 9, 7 ( ) − 125. Vertex: (4, 13); concave down 126. Center: 5, 2; ( ) − radius: 8 127. 7 128. Odd 5.6 Assess Your Understanding (page 341) 5. 16 { } 7. 16 5 { } 9. 5 { } − 11. 64, 64 { } − 13. 6, 7 { } − 15. 64 { } 17. 1 3{ } 19. 3 { } − 21. 5{ } 23. 16 3 { } 25. 6 { } − 27. 2 { } − 29. e 1 1 4 { } − + + 31. 15 5 13 2 { } − + 33. 2{ } 35. 9 2{ } 37. 7{ } 39. 2 4 2 { } − + 41. 3, 3 { } − 87. y Cx = 89. y Cx x 1 ( ) = + 91. y Ce x3 = 93. y Ce 3 x4 = + − 95. y C x x 2 1 4 3 1 6 1 9 ( ) ( ) = + + 97. 3 99. 1 85. (a) f g x x x x ; is any real number ( ) { } ( ) = or , ( ) −∞ ∞ (b) g f x x x x ; 0 ( )( ) { } = > or 0, ( )∞ (c) 5 (d) f h x x x x ln ; 0 or , 0 0, 2 ( )( ) { } ( ) ( ) = ≠ −∞ ∪ ∞ (e) 2
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