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Section 3.2 Logarithmic Functions and Their Graphs 209
73.
gx lnx
Domain: x > 0 ⇒ x < 0
The domain is , 0.
Vertical asymptote: x 0 ⇒ x 0
x-intercept:
0 lnx
e 0 x
1 x
The x-intercept is 1, 0.
5
4
3
2
1
−8 −7 −6 −5 −4 −3 −2 −1 1 2
−2
−3
−4
−5
y
x
74.
fx ln3 x
Domain: 3 x > 0 ⇒ x < 3
The domain is , 3.
Vertical asymptote: 3 x 0 ⇒ x 3
x-intercept:
ln3 x 0
e 0 3 x
1 3 x
2 x
The x-intercept is 2, 0.
y ln3 x ⇒ x 3 e y
x 2.95 2.86 2.63 2 0.28
y 3 2 1 0 1
5
4
3
2
−6 −5 −4 −3 −2 −1 1 2 4
−2
−3
−4
−5
y
x
75. gx lnx 3 is a horizontal shift three units 76. gx lnx 4 is a horizontal shift four units
to the left.
to the right.
77. gx ln x 5 is a vertical shift five units
78. gx ln x 4 is a vertical shift four units
downward.
upward.
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79. gx lnx 1 2 is a horizontal shift one unit 80. gx lnx 2 5 is a horizontal shift
to the right and a vertical shift two units upward.
two units to the left and a vertical shift five units
downward.
81.
f(x x 2 ln x 4
(a)
−1
7
−1
(b) Domain: 0,
(c) Increasing on 2,
Decreasing on 0, 2
(d) Relative minimum: 2, 1.693
11
82.
gx
(a)
7
−1
−1
12 ln x
x
(b) Domain: 0,
(c) Increasing on 0, 2.72
Decreasing on 2.72,
(d) Relative maximum: 2.72, 4.41
11