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: 27


(a) $x=\frac{1}{5}\log\frac{5}{4}$ (b) $x\approx 0.019382$

Work Step by Step

(a) We need to solve: $4(1+10^{5x})=9$ $1+10^{5x}=\frac{9}{4}$ $10^{5x}=\frac{9}{4}-1$ $10^{5x}=\frac{5}{4}$ We take the log of both sides and use log rules to simplify: $\log 10^{5x}=\log \frac{5}{4}$ $5x=\log\frac{5}{4}$ $x=\frac{1}{5}\log\frac{5}{4}$ (b) We solve using a calculator: $x\approx 0.019382$
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