Answer
$x=1$
Work Step by Step
Note that $27=3^3$.
Write $27$ as $3^3$ to obtain:
$3^{2x+1}=3^3$
RECALL:
If $a^x = a^y$, then $x=y$.
Use the rule above to obtain:
$3^{2x+1}=3^3
\\2x+1=3
\\2x=3-1
\\2x=2
\\x=\frac{2}{2}
\\x=1$