College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 404: 13


(a) $x \approx -0.460517$ (b) $x\approx -0.602060$

Work Step by Step

(a) Take the natural logarithm of both sides to obtain: $\ln{e^{-5x}} = \ln{10}$ Use the rule $\ln{e^n} = n$ to obtain: $-5x = \ln{10} \\\dfrac{-5x}{-5}=\dfrac{\ln{10}}{-5} \\x=\dfrac{\ln{10}}{-5}$ Use the rule $\log{(a^n)} = n\log{a}$ to obtain: $x \approx -0.460517$ (b) Use a calculator to evaluate the answer and have: $x =-2(0.3010299957) \\x\approx -0.602060$
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