Solve for x 9^x=243

$9^{x} = 243$

Step 1

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

$3^{2 x} = 3^{5}$

Step 2

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

$2 x = 5$

Step 3

Divide each term in $2 x = 5$ by $2$ and simplify.

Divide each term in $2 x = 5$ by $2$ .

$\frac{2 x}{2} = \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{5}{2}$

Divide $x$ by $1$ .

$x = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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