Solve for x 9^x=27^2

$9^{x} = 27^{2}$

Create equivalent expressions in the equation that all have equal bases.

$3^{2 x} = 3^{3 \cdot 2}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$2 x = 3 \cdot 2$

Solve for $x$ .

Multiply $3$ by $2$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$