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264 Chapter 3 Exponential and Logarithmic Functions<br />

124.<br />

126.<br />

lnx 8 3 125.<br />

1<br />

lnx 8 3<br />

2<br />

lnx 8 6<br />

x 8 e 6<br />

x e 6 8 395.429<br />

log 5 x 2 log 5 x log 5 x 5 127.<br />

x <br />

log 5 x 2<br />

x log 5x 5<br />

x 2<br />

x<br />

x 2 4x 2 0<br />

4 ± 16 42<br />

2<br />

x 2 6 0.449<br />

(Other zero is extraneous.)<br />

x 5<br />

x 2 x 2 5x<br />

2 ± 6<br />

log 4 x 1 log 4 x 2 log 4 x 2<br />

log 4 x 1 log 4 x 2<br />

x 2<br />

No solution<br />

x 1 x 2<br />

x 2<br />

x 1x 2 x 2<br />

x 2 x 2 x 2<br />

x 2 0<br />

x 0<br />

log 10 1 x 1<br />

10 1 1 x<br />

(extraneous)<br />

x 1 10 1 0.9<br />

128.<br />

log 10 x 4 2 129.<br />

x 4 10 2 100<br />

x 104<br />

x 104<br />

xe x e x 0<br />

x 1e x 0<br />

x 1 0 since e x 0<br />

x 1<br />

130.<br />

132.<br />

2xe 2x e 2x 0 131.<br />

2x 1e 2x 0<br />

2x 1 0 since e 2x 0<br />

1 ln x<br />

x 2 0<br />

1 ln x 0 since x > 0<br />

ln x 1<br />

x 1 2<br />

x e 2.718<br />

x ln x x 0<br />

xln x 1 0<br />

ln x 1 0 since x > 0<br />

ln x 1<br />

x e 1 1 e 0.368<br />

133. 37550 7550e 0.0725t<br />

3 e 0.0725t<br />

ln 3 0.0725t<br />

t ln 3 15.2 years<br />

0.0725<br />

© Houghton Mifflin Company. All rights reserved.

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