Evaluate 9^x-1=2

$9^{x} - 1 = 2$

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

Add $1$ to both sides of the equation.

$9^{x} = 2 + 1$

Add $2$ and $1$ .

$9^{x} = 3$

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

$3^{2 x} = 3^{1}$

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

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$