Answer
$x=2$
Work Step by Step
RECALL:
$\log_a{x}=y \longrightarrow a^y = x$
Use the rule above to obtain:
$\log_3{243}=2x +1
\\\longrightarrow 3^{2x+1}=243$
Note that $243=3^5$. Thus, the expression above is equivalent to:
$3^{2x+1}=3^5$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$2x+1=5$
Subtract 1 on both sides of the equation to obtain:
$2x=4$
Divide by 2 on both sides of the equation to obtain:
$x=2$
