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Section 3.2 Logarithmic Functions and Their Graphs 213
110. (a)
4
y = lnx
y 3
8
−4
y 1
y2
−4
(b) Pattern is x 1 1 2x 1 2 1 3x 1 3 1 4x 1 4 . . . .
4
y = lnx
−4
8
y 4
−4
As you use more terms, the graph better approximates the graph of ln x on the interval 0, 2.
111.
f x ln x
x
(a)
x 1 5 10 10 2 10 4 10 6
f x 0 0.322 0.230 0.046 0.00092 0.0000138
(b) As x increases without bound, fx approaches 0.
(c)
0.5
0
0
100
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112.
ft 75 6 lnt 1
60 75 6 lnt 1
lnt 1 15
6 5 2
t e 52 1 11.18
Or, you could graph f t and y 60 together in
the same viewing window, and determine their
point of intersection.
114. 2x 2 3x 5 2x 5x 1
116.
16x 2 16x 7
x
16 ± 256 448
32
1 2 ± 3
4 i
x 1 2 3
4 i x 1 2 3
4 i
113. x 2 2x 3 x 3x 1
115. 12x 2 5x 3 4x 33x 1
117. 16x 2 25 4x 5 4x 5
118. 36x 2 49 6x 76x 7