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Section 3.2 Logarithmic Functions and Their Graphs 207
47.
y log 2 x 2
48.
y log 2 x 1
Domain: x 2 > 0 ⇒ x > 2
Vertical asymptote: x 2
log 2 x 2 0
x 2 1
x 1
x-intercept: 1, 0
5
4
3
2
1
−5 −4 −3 −2 1 2 3 4 5
y
x
Domain: x 1 > 0 ⇒ x > 1
Vertical asymptote: x 1
log 2 x 1 0
x 1 1
x 2
x-intercept: 2, 0
5
4
3
2
1
y
−1 1 2 3 4 5 6 7 8 9
x
−2
−3
−4
−5
−2
−3
−4
−5
49.
y 1 log 2 x 50.
y 2 log 2 x
Domain: x > 0
Vertical asymptote: x 0
1 log 2 x 0
log 2 x 1
x 2 1 1
x-intercept: 1 2 , 0
2
5
4
3
2
1
y
−1 1 2 3 4 5 6 7 8 9
−2
−3
−4
−5
x
Domain: x > 0
Vertical asymptote: x 0
2 log 2 x 0
log 2 x 2
x 2 2 4
x-intercept: 4, 0
8
7
6
5
4
3
2
1
y
−1 1 2 3 4 9
−2
x
51.
y 1 log 2 x 2 52.
y 2 log 2 x 1
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53.
Domain: x 2 > 0 ⇒ x > 2
Vertical asymptote: x 2 y
1 log 2 x 2 0
log 2 x 2 1
x 2 2 1 1 2
x 5
x-intercept: 5 2 , 0
2
5
4
3
2
1
−1 1 3 4 5 6 7 8 9
−2
−3
−4
−5
x
Domain: x 1 > 0 ⇒ x > 1
Vertical asymptote: x 1
2 log 2 x 1 0
log 2 x 1 2
x 1 2 2 1 4
x 3
x-intercept: 3 4 , 0
4
7
6
5
4
3
2
y
−3 −2 1 2 3 4 5 6 7
fx log 3 x 2 54. fx log 3 x
55. fx log 3 x 2
Asymptote: x 0
Asymptote: x 0
Asymptote: x 2
Point on graph: 1, 2
Point on graph: 1, 0
Point on graph: 1, 0
Matches graph (b).
Matches graph (c).
Matches graph (d).
x