Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 12 - Exponential Functions and Logarithmic Functions - Connecting: The Concepts - Exercises - Page 824: 6


$x\approx 0.2524$

Work Step by Step

Solving $\mathrm{a}^{t}=b$ FOR $t$ ... Take the logarithm (either natural or common) on both sides. $\log(3^{5x})=\log 4\qquad$ ... apply $\log_{a}M^{p}=p\cdot\log_{a}M$ $5x\cdot\log 3=\log 4 \qquad$ ... divide with $(5\log 3)$ $x=\displaystyle \frac{\log 4}{5\log 3}\approx 0.252371901429$ $x\approx 0.2524$
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