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 4.4 Logarithmic Functions - 4.4 Assess Your Understanding - Page 322: 97



Work Step by Step

$\because y=\log_a x \text{ is equivalent to } x= a^y$ $\therefore 2x+1 = \log_3 243 \text{ is equivalent to } 243=3^{2x+1}$ With $243=3^5$, solve the equation above using the rule $a^m=a^n\implies m=n$ to obtain: \begin{align*} 243&=3^{2x+1}\\\\ 3^5&=3^{2x+1}\\\\\ 5&=2x+1\\\\ 5-1&=2x\\\\ 4&=2x\\\\ \frac{4}{2}&=\frac{2x}{2}\\\\ 2&=x \end{align*}
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