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

$2$
$\because y=\log_a x \text{ is equivalent to } x= a^y$ $\therefore 2x+1 = \log_3 243 \text{ is equivalent to } 243=3^{2x+1}$ 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*}