Answer
$x=\frac{3}{2}$
Work Step by Step
We are given the exponential equation $9^{x}=27$.
We can express each side using a common base and then solve for $x$.
$9^{x}=(3^{2})^{x}=3^{2x}$
$27=3^{3}$
$3^{2x}=3^{3}$
Take the natural log of both sides.
$ln(3^{2x})=ln(3^{3})$
$2xln(3)=3ln(3)$
Divide both sides by $ln(3)$.
$2x=3$
Divide both sides by 2.
$x=\frac{3}{2}$