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262 Chapter 3 Exponential and Logarithmic Functions<br />
90.<br />
5 lnx 2 lnx 2 3 lnx lnx 2 5 lnx 2 lnx 3<br />
ln <br />
x 2 5<br />
x 2x 3<br />
91. ln 3 1 3 ln4 x2 ln x ln <br />
34 x 2 13<br />
x ln 3 4 3 x 2<br />
x<br />
<br />
92.<br />
3ln x 2 lnx 2 1 2 ln 5 ln x 3 lnx 2 1 6 ln 5 2<br />
ln<br />
25x 3<br />
x 2 1 6<br />
93.<br />
s 25 <br />
13 lnh12<br />
ln 3<br />
(a)<br />
60<br />
(b)<br />
h 4 6 8 10 12 14<br />
s 38 33.2 29.8 27.2 25 23.2<br />
2<br />
0<br />
15<br />
(c) As the depth increases, the number of miles of roads<br />
cleared decreases.<br />
94.<br />
ft 85 14 log 10 t 1<br />
71 85 14 log 10 t 1<br />
log 10 t 1 1<br />
t 9 months<br />
95. 8 x 512 8 3 ⇒ x 3<br />
96. 3 x 729 3 6 ⇒ x 6<br />
97. 6 x 1<br />
216 1 6 3 63 ⇒ x 3<br />
98. 6 x2 1296 6 4 ⇒ x 2 4 ⇒ x 6<br />
99. 2 x1 1 16<br />
2 x1 2 4<br />
x 1 4<br />
x 5<br />
101. log 7 x 4 ⇒ x 7 4 2401<br />
103. log 2 x 1 3 104.<br />
2 3 x 1<br />
x 9<br />
100.<br />
102. log x 243 5 ⇒ x 5 243 3 5 ⇒ x 3<br />
log 5 2x 1 2 105.<br />
5 2 2x 1<br />
2x 24<br />
x 12<br />
4 x2 64<br />
4 x2 4 3<br />
x<br />
2 3<br />
x 6<br />
ln x 4<br />
x e 4 54.598<br />
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