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Section 3.4 Solving Exponential and Logarithmic Equations 235<br />
108.<br />
x 4 5 6 7 8<br />
109.<br />
6 log 3 0.5x 11<br />
f x<br />
8.99 9.66 10.20 10.67 11.07<br />
x 12 13 14 15 16<br />
12<br />
f x<br />
9.79 10.22 10.63 11.00 11.36<br />
14<br />
−4<br />
0<br />
14<br />
x 5.606<br />
0<br />
0<br />
x 14.988<br />
21<br />
110.<br />
x 150 155 160 165 170<br />
f x 10.85 10.92 10.99 11.06 11.13<br />
14<br />
x 160.489<br />
0<br />
0<br />
200<br />
111.<br />
log 10 x x 3 3<br />
Graphing y log 10 x x 3 3, you obtain<br />
two zeros, x 1.469 and x 0.001.<br />
112. Solving y log 10 x 2 4 0, x ±100.<br />
113.<br />
ln x lnx 2 1 114.<br />
Graphing y ln x lnx 2 1, you obtain<br />
one zero, x 2.928.<br />
ln x lnx 1 2<br />
Graphing y ln x lnx 1 2, you obtain<br />
one zero, x 2.264.<br />
115.<br />
lnx 3 lnx 3 1<br />
Graphing y lnx 3 lnx 3 1, you<br />
obtain x 3.423.<br />
116. ln x lnx 2 4 10<br />
Solving y ln x lnx 2 4 10 0,<br />
x 27.984.<br />
117.<br />
y 1 7<br />
10<br />
118.<br />
y 1 4<br />
8<br />
© Houghton Mifflin Company. All rights reserved.<br />
119.<br />
121.<br />
y 2 2 x1 5<br />
Intersection: 4.585, 7<br />
y 1 80<br />
y 2 4e 0.2x<br />
Intersection:<br />
14.979, 80<br />
y 1 3.25<br />
−12<br />
−30<br />
4<br />
y 1<br />
y 2<br />
−6<br />
100<br />
y 1<br />
y 2<br />
−10<br />
y 1<br />
12<br />
30<br />
120.<br />
y 2 3 x1 2<br />
The graphs intersect<br />
at x, y 0.631, 4.<br />
y 1 500<br />
y 2 1500e x2<br />
From the graph, we have<br />
x, y 2.197, 500.<br />
−9<br />
−2<br />
800<br />
−200<br />
y 2<br />
−4<br />
y 1<br />
y 2<br />
y 1<br />
9<br />
10<br />
y 2 1 2 lnx 2<br />
Intersection:<br />
0<br />
663.142, 3.25<br />
0<br />
y 2<br />
700
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