#### Answer

$x=\dfrac{3}{2}$

#### Work Step by Step

Using the laws of exponents, the given equation, $
9^x=27
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3^2)^x=3^3
\\\\
3^{2x}=3^3
.\end{array}
Since the bases are the same, the exponents can be equated. Hence,
\begin{array}{l}\require{cancel}
2x=3
\\\\
x=\dfrac{3}{2}
.\end{array}