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208 Chapter 3 Exponential and Logarithmic Functions
56.
fx log 3 1 x
Asymptote: x 1
Domain: 1 x > 0 ⇒ x < 1
Point on graph: 0, 0
Matches graph (a).
57.
f x log 10 x
gx log 10 x is a reflection
in the x-axis of the graph of f.
58. The graph of
gx log 10 x 7 is a horizontal
shift 7 units to the left
of the graph of f x log 10 x.
59. f x log 2 x 60. The graph of gx log 2 x 3 is a vertical shift
gx 4 log 2 x is obtained from f by a
reflection in the x-axis followed by a vertical
shift four units upward.
three units upward of the graph of f x log 2 x.
61. Horizontal shift three units to the left and a vertical
shift two units downward
62. Horizontal shift one unit to the right and a vertical
shift four units upward
63. ln42 1.869 64. ln 18.31 2.907 65. ln 1 2 0.693 66. 3 ln0.75 0.863
67.
ln e 2 2 68. ln e 1 69. e ln 1.8 1.8
70.
(Inverse Property)
(Inverse Property)
7 ln e 0 7 ln 1
70 0
71.
f x lnx 1
Domain: x > 1
Vertical asymptote:
x-intercept: 2, 0
x 1
5
4
3
2
1
y
−2 −1 2 3 4 5 6 7 8
x
−2
−3
−4
−5
72.
hx lnx 1
y lnx 1 ⇒ e y 1 x
Domain: x 1 > 0 ⇒ x > 1
The domain is 1, .
Vertical asymptote: x 1 0 ⇒ x 1
x-intercept:
lnx 1 0
0 x
The x-intercept is 0, 0.
e 0 x 1
1 x 1
x 0.39 0 1.72 6.39 19.09
y 1 2 0 1 2 3
5
4
3
2
1
y
−3 −2 1 2 3 4 5 6 7
x
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