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: 25


(a) $x=\frac{14\log 0.1}{\log 3}$ (b) $x\approx-29.342646$

Work Step by Step

(a) We need to solve: $3^{x/14}=0.1$ We take the log of both sides and use log rules to simplify: $\log 3^{\frac{x}{14}}=\log 0.1$ $(\frac{x}{14})\log 3=\log 0.1$ $\frac{x}{14}=\frac{\log 0.1}{\log 3}$ $x=\frac{14\log 0.1}{\log 3}$ (b) We solve using a calculator: $x\approx -29.342646$
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