Solve for x 9^(2x-2)=81

$9^{2 x - 2} = 81$

Step 1

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

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

Step 2

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

$2 x - 2 = 2$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$2 x = 2 + 2$

Add $2$ and $2$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$