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220 Chapter 3 Exponential and Logarithmic Functions
78.
y 1 ln x 1 2 lnx 1, y 2 lnxx 1, x > 0 x 0 1 2 5 10
(a)
5
(b)
−2
10
y 1
y 2
ERROR 0.34657 1.2425 2.5053 3.5015
ERROR 0.34657 1.2425 2.5053 3.5015
−3
(c) The graphs and table suggest that y 1 y 2 .
In fact,
y 1 ln x 1 2 lnx 1 ln x lnx 112 lnxx 1 y 2 .
79.
y 1 ln x 2
y 2 2 ln x
(a)
−9
6
−6
The domain of y 2 is x > 0.
9
(b)
x 8 4 1 2 4
y 1 4.1589 2.7726 0 1.3863 2.7726
y 2 undefined undefined 0 1.3863 2.7726
(c) The graphs and table suggest that y 1 y 2 for x > 0.
The functions are not equivalent because the domains
are different.
80.
y 1 1 4 lnx 4 x 2 1, y 2 ln x 1 4 lnx2 1
(a)
6
−9
9
−6
(b)
x 10 1 0 1 5 10
y 1
y 2
3.4564 0.17329 ERROR 0.17329 2.4240 3.4564
ERROR ERROR ERROR 0.17329 2.4240 3.4564
(c) No, the expressions are not equivalent. The domain of y 1 is all x 0, whereas the
domain of y 2 is x > 0.
81. log 3 9 2 log 3 3 2
83. log 4 16 3.4 3.4 log 4 4 2 6.8 log 4 4 6.8
85. log 2 4 is undefined. 4 is not in the domain of
f x log 2 x.
87. log 5 75 log 5 3 log 75 5 3 log 5 25 log 5 52 2
89. ln e 3 ln e 7 3 7 4
82. log 6 3 6 log 6 6 13 1 3 log 6 6 1 31 1 3
84. log 5 1
125 log 5 5 3 3 log 5 5 31 3
86. log 4 16 is undefined because 16 is not in the
domain of log 4 x.
88.
log 4 2 log 4 32 log 4 4 12 log 4 4 52
1 2 log 4 4 5 2 log 4 4
1 21 5 21
3
90. ln e 6 2 ln e 5 6 ln e 10 ln e 6 10 4
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91. 2 ln e 4 24 ln e 8
92. ln e 4.5 4.5 ln e 4.5