Answer
$x=\frac{3}{2}$
Work Step by Step
Note that:
$9=3^2$
AND
$27=3^3$
Write each side with a base of $3$ to obtain:
$(3^2)^{x}=3^3
\\3^{2x}=3^3$
RECALL:
If $a^x = a^y$, then $x=y$.
Use the rule above to obtain:
$3^{2x}=3^3
\\2x=3
\\x=\frac{3}{2}$