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Section 3.4 Solving Exponential and Logarithmic Equations 231 70. 525 1 e x 525 275 e 250 275 10 x 525 275 1 11 x ln 10 11 x ln 10 11 ln 11 10 0.095 40 200 1 5e0.01x 1 5e 0.01x 40 200 1 5 5e 0.01x 4 5 e 0.01x 4 25 0.01x ln 4 25 x ln425 0.01 1 e x 275 71. x 183.258 72. 50 e 3x 12 1 2e 0.001x 1000 73. x 0.828 1 2e 0.001x 50 1000 0.05 x 0.6 0.7 0.8 0.9 1.0 f x 6.05 8.17 11.02 14.88 20.09 2e 0.001x 0.95 e 0.001x 0.475 16 0.001x ln 0.475 ln 0.475 x 0.001 −3 −2 3 x 744.440 74. e 2x 50 75. 20100 e x2 500 © Houghton Mifflin Company. All rights reserved. 76. −6 x 1.6 1.7 1.8 1.9 2.0 e 2x 24.53 29.96 36.60 44.70 54.60 −5 x 1.956 70 6 −2 x 5 6 7 8 9 f x 1756 1598 1338 908 200 2200 −200 x 8.635 400 x 350 1 e x 0 1 2 3 4 400 400 1 e x 200 292 352 381 393 12 −2 0 4 x 1.946
232 Chapter 3 Exponential and Logarithmic Functions 77. 1 0.065 365 365t 4 ⇒ t 21.330 78. 4 2.471 40 9t 21 3.938225 9t 21 The zero of y 3.938225 9t 21 is t 0.247. 79. 3000 80. 119 e 6x 14 7 gx 6e 1x 25 The zero of y 3000 2 e 2 2x is x 3.656. 2 e 2x 2 81. Zero at x 0.427 The zero of y 119 e 6x 14 7 is x 0.572. −6 6 15 −30 82. fx 3e 3x2 962 83. gt e 0.09t 3 84. The zero is x 3.847. 1000 8 ht e 0.125t 8 The zero is t 16.636. 10 −20 40 −10 10 −4 24 −1100 −4 Zero at t 12.207 −10 85. ln x 3 86. ln x 2 87. ln 4x 2.1 x e 3 0.050 x e 2 1 e 2 0.135 4x e 2.1 x 1 2.042 4 e2.1 88. ln 2x 1.5 89. 2 2 ln 3x 17 90. 3 2 ln x 10 e 1.5 2x 2 ln 3x 19 2 ln x 7 91. x 1 2 e1.5 2.241 log 5 3x 2 log 5 6 x 92. 3x 2 6 x 4x 4 x 1 ln 3x 19 2 3x e 192 x 1 3 e192 x 4453.242 log 9 4 x log 9 2x 1 93. 4 x 2x 1 x 5 ln x 7 2 3.5 x e 3.5 33.115 log 10 z 3 2 z 3 10 2 z 10 2 3 103 © Houghton Mifflin Company. All rights reserved.
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232 Chapter 3 Exponential and Logarithmic Functions<br />
77. 1 0.065<br />
365 365t 4 ⇒ t 21.330 78.<br />
4 2.471<br />
40 9t 21<br />
3.938225 9t 21<br />
The zero of y 3.938225 9t 21 is t 0.247.<br />
79.<br />
3000<br />
80.<br />
119<br />
e 6x 14 7<br />
gx 6e 1x 25<br />
The zero of y 3000<br />
2 e 2 2x<br />
is x 3.656.<br />
2 e 2x 2 81. Zero at x 0.427<br />
The zero of y 119<br />
e 6x 14 7<br />
is x 0.572.<br />
−6<br />
6<br />
15<br />
−30<br />
82.<br />
fx 3e 3x2 962 83. gt e 0.09t 3<br />
84.<br />
The zero is x 3.847.<br />
1000<br />
8<br />
ht e 0.125t 8<br />
The zero is t 16.636.<br />
10<br />
−20<br />
40<br />
−10<br />
10<br />
−4<br />
24<br />
−1100<br />
−4<br />
Zero at t 12.207<br />
−10<br />
85.<br />
ln x 3 86. ln x 2<br />
87.<br />
ln 4x 2.1<br />
x e 3 0.050<br />
x e 2 1 e 2 0.135<br />
4x e 2.1<br />
x 1 2.042<br />
4 e2.1<br />
88.<br />
ln 2x 1.5 89. 2 2 ln 3x 17<br />
90.<br />
3 2 ln x 10<br />
e 1.5 2x<br />
2 ln 3x 19<br />
2 ln x 7<br />
91.<br />
x 1 2 e1.5 2.241<br />
log 5 3x 2 log 5 6 x 92.<br />
3x 2 6 x<br />
4x 4<br />
x 1<br />
ln 3x 19 2<br />
3x e 192<br />
x 1 3 e192<br />
x 4453.242<br />
log 9 4 x log 9 2x 1 93.<br />
4 x 2x 1<br />
x 5<br />
ln x 7 2 3.5<br />
x e 3.5 33.115<br />
log 10 z 3 2<br />
z 3 10 2<br />
z 10 2 3<br />
103<br />
© Houghton Mifflin Company. All rights reserved.
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