Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Review Exercises - Page 513: 68


$ x\approx 4.52$

Work Step by Step

$8^{x}=12,143$ We can't show the RHS as a power of 8, so we apply $\log_{8}($...$)$ to both sides $\log_{8}8^{x}=\log_{8}12,143\qquad $ ... apply basic property, $\log_{b}b^{x}=x $ $ x=\log_{8}12,143$ if your calculator has only $\ln $ and $\log $, apply the change of base property, $\displaystyle \log_{b}M=\frac{\log_{a}M}{\log_{a}b}$ and round to two decimal places: $ x=\displaystyle \frac{\log 12,143}{\log 8}\approx 4.52$
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