#### Answer

$2$

#### 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*}