Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.6 Logarithmic and Exponential Equations - 4.6 Assess Your Understanding - Page 337: 54


$x \approx - 0.297$

Work Step by Step

Recall the logarithmic property: $\log m^n= n \log m$ To find the value of $x$, we apply $\log$ to both sides and then isolate $x$ as follows: $\log 0.3^{1+x}=\log 1.7^{2x-1} \\ (1+x)\log 0.3=(2x-1)\log 1.7 \\ \log 0.3+x\log 0.3=2x\log 1.7-\log 1.7 \\ \log 0.3+\log 1.7=x(2\log 1.7 -\log 0.3)$ or, $x=\displaystyle \frac{\log 0.3+\log 1.7}{2\log 1.7 -\log 0.3}\approx - 0.297$ Thus, our answer is: $x \approx - 0.297$
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