Solve for x 9^(2x)=27

$9^{2 x} = 27$

Step 1

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

$3^{2 (2 x)} = 3^{3}$

Step 2

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

$2 (2 x) = 3$

Step 3

Solve for $x$ .

Multiply $2$ by $2$ .

$4 \cdot x = 3$

Divide each term in $(4 \cdot x) = 3$ by $4$ and simplify.

Divide each term in $(4 \cdot x) = 3$ by $4$ .

$\frac{(4 \cdot x)}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$