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218 Chapter 3 Exponential and Logarithmic Functions<br />
58.<br />
y 1 ln <br />
x<br />
(a)<br />
x 2 , y 2 1 2 ln x lnx 2<br />
5<br />
(b)<br />
x 3 4 5 6 10 20<br />
−2<br />
10<br />
y 1 0.5493 0 0.2939 0.4904 0.9281 1.393<br />
y 2 0.5493 0 0.2939 0.4904 0.9281 1.393<br />
−3<br />
(c) The graphs and table suggest that y 1 y 2 .<br />
In fact,<br />
y 1 ln <br />
x<br />
x 2 ln x12 lnx 2 1 2 ln x lnx 2 y 2 .<br />
59. ln x ln 4 ln 4x61. 60. ln y ln z ln yz<br />
log 4 z log 4 y log z 4<br />
y<br />
62. log 5 8 log 5 t log 5 8 t<br />
63. 2 log 2 x 3 log 2 x 3 2<br />
64.<br />
5<br />
2 log 7z 4 log 7 z 4 52<br />
65.<br />
1<br />
2 lnx2 4 lnx 2 4 12 66.<br />
lnx 2 4<br />
2 ln x lnx 1 ln x 2 lnx 1<br />
lnx 2 x 1<br />
lnx 3 x 2 <br />
67.<br />
ln x 3 lnx 1 ln x lnx 1 3<br />
68.<br />
ln x 2 lnx 2 ln x lnx 2 2<br />
ln<br />
x<br />
x 1 3<br />
ln<br />
x<br />
x 2 2<br />
69. lnx 2 lnx 2 ln <br />
x 2<br />
x 2<br />
71.<br />
72.<br />
ln x 2lnx 2 lnx 2 ln x 2 lnx 2x 2<br />
ln x 2 lnx 2 4<br />
ln x lnx 2 4 2<br />
ln<br />
x<br />
x 2 4 2<br />
4ln z lnz 5 2 lnz 5 4ln zx 5 lnz 5 2<br />
70.<br />
lnzz 5 4 lnz 5 2<br />
ln z4 z 5 4<br />
z 5 2<br />
3 ln x 2 ln y 4 ln z ln x 3 ln y 2 ln z 4<br />
ln x 3 y 2 ln z 4<br />
ln x3 y 2<br />
z 4<br />
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