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Section 3.3 Properties of Logarithms 219
73.
1
3 2 lnx 3 ln x lnx2 1 1 3 lnx 32 ln x lnx 2 1
1 3 lnxx 32 lnx 2 1
1 3
ln
xx 32
x 2 1
xx
ln 3 32
x 2 1
74.
2ln x lnx 1 lnx 1 2 ln
2 ln
2 ln
x
x 1 lnx 1
x
x 1x 1
x
x 2 1
ln
x
x 2 1 2
75.
1
3 ln y 2 lny 4 lny 1 1 3 ln y lny 42 lny 1
1 3 lny y 42 lny 1
ln 3 y y 4 2 ln y 1
ln
3yy 4 2
y 1
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76.
77.
1
2lnx 1 2 lnx 1 3 ln x 1 2lnx 1 lnx 1 2 ln x 3
y 1 2ln 8 lnx 2 1
y 2 ln
64
x 2 1 2
(a)
(b)
−9
6
−6
9
1 2lnx 1x 1 2 ln x 3
lnx 1x 1 2 12 ln x 3
lnx 1 12 x 1 ln x 3
lnx 3 x 1x 1
(c) The graphs and table suggest that y 1 y 2 . In fact,
y 1 2ln 8 lnx 2 1
2 ln
8
x 2 1 ln 64
x 2 1 2 y 2 .
x 8 4 2 0 2 4 8
y 1 4.1899 1.5075 0.9400 4.1589 0.9400 1.5075 4.1899
y 2 4.1899 1.5075 0.9400 4.1589 0.9400 1.5075 4.1899