Solve for x 3^(2x)+12=39

$3^{2 x} + 12 = 39$

Step 1

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

Subtract $12$ from both sides of the equation.

$3^{2 x} = 39 - 12$

Subtract $12$ from $39$ .

$3^{2 x} = 27$

Step 2

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

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

Step 3

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

$2 x = 3$

Step 4

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

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