Answer
$x=\dfrac{7}{2}$
Work Step by Step
Express both sides of the equation with the same base. Once the bases are the same, then equate the exponents. That is,
\begin{array}{l}
9^{x-2}=27\\\\
(3^2)^{x-2}=3^3\\\\
3^{2x-4}=3^3\\\\
2x-4=3\\\\
2x=7\\\\
x=\dfrac{7}{2}
.\end{array}
