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Building Skills

9. $\log_{5} 25 = 2$ $\log_{5} 25 = 2$
11. $\log_{1 / 16} 4 = - \frac{1}{2}$ $\log_{1 / 16} 4 = - \frac{1}{2}$
13. $\log_{10} 1 = 0$ $\log_{10} 1 = 0$
15. $\log_{10} 0.1 = - 1$ $\log_{10} 0.1 = - 1$
17. $\log_{a} 5 = 2$ $\log_{a} 5 = 2$
19. $\log_{a} (13 / 2) = 3$ $\log_{a} (13 / 2) = 3$
21. $2^{5} = 32$ $2^{5} = 32$
23. $10^{2} = 100$ $10^{2} = 100$
25. $10^{0} = 1$ $10^{0} = 1$
27. $10^{- 2} = 0.01$ $10^{- 2} = 0.01$
29. $8^{1 / 3} = 2$ $8^{1 / 3} = 2$
31. $e^{x} = 2$ $e^{x} = 2$
33. 3
35. 4
37. $- 3$ $- 3$
39. $\frac{3}{2}$ $\frac{3}{2}$
41. $\frac{1}{4}$ $\frac{1}{4}$
43. 0
45. 1
47. 7
49. 5
51. 4
53. 8
55. $(- 1, \infty)$ $(- 1, \infty)$
57. $(1, \infty)$ $(1, \infty)$
59. $(2, \infty)$ $(2, \infty)$
61. (1, 2)
63. $(- \infty, 0) \cup (0, \infty)$ $(- \infty, 0) \cup (0, \infty)$
65. $(12, \infty)$ $(12, \infty)$
67. $(- \infty, - 1) \cup (0, \infty)$ $(- \infty, - 1) \cup (0, \infty)$
69. $(- \infty, - 1) \cup (2, \infty)$ $(- \infty, - 1) \cup (2, \infty)$
71.
1. f
2. a
3. d
4. b
5. e
6. c
73. $Domain = (- 3, \infty) Range = (- \infty, \infty)$ $Domain = (- 3, \infty) Range = (- \infty, \infty)$ Asymptote: $x = - 3$ $x = - 3$
75. Domain: $(1, \infty);$ $(1, \infty);$ range: $(- \infty, \infty);$ $(- \infty, \infty);$ asymptote: $x = 1$ $x = 1$
77. $Domain = (0, \infty) Range = (- \infty, \infty)$ $Domain = (0, \infty) Range = (- \infty, \infty)$ Asymptote: $x = 0$ $x = 0$
79. Domain: $(1, \infty);$ $(1, \infty);$ range: $(- \infty, \infty);$ $(- \infty, \infty);$ asymptote: $x = 1$ $x = 1$
81. Domain: $(- \infty, 0);$ $(- \infty, 0);$ range: $(- \infty, \infty);$ $(- \infty, \infty);$ asymptote: $x = 0$ $x = 0$
83. $Domain = (0, \infty) Range = [0, \infty)$ $Domain = (0, \infty) Range = [0, \infty)$ Asymptote: $x = 0$ $x = 0$
85. $Domain = (1, \infty) Range = (- \infty, \infty)$ $Domain = (1, \infty) Range = (- \infty, \infty)$ Asymptote: $x = 1$ $x = 1$
87. $Domain = (- \infty, 3) Range = (- \infty, \infty)$ $Domain = (- \infty, 3) Range = (- \infty, \infty)$ Asymptote: $x = 3$ $x = 3$
89. Domain: $(0, \infty);$ $(0, \infty);$ range: $(- \infty, \infty);$ $(- \infty, \infty);$ Asymptote: $x = 0$ $x = 0$
91. $Domain = (- \infty, 3) Range = (- \infty, \infty)$ $Domain = (- \infty, 3) Range = (- \infty, \infty)$ Asymptote: $x = 3$ $x = 3$
93. 1
95. 2
97. 4
99.
101.
103.
105.
107. Horizontal shift to the left by 1 and reflection about the x-axis
109.
1. 102
2. 2020
3. The price decreases faster in the beginning, but then the decreases in price become slower as time goes on.