Solve for x 3^(2x)=27^4

$3^{2 x} = 27^{4}$

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

$3^{2 x} = 3^{3 \cdot 4}$

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

$2 x = 3 \cdot 4$

Solve for $x$ .

Multiply $3$ by $4$ .

$2 x = 12$

Divide each term in $2 x = 12$ by $2$ and simplify.

Divide each term in $2 x = 12$ by $2$ .

$\frac{2 x}{2} = \frac{12}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{12}{2}$

Divide $x$ by $1$ .

$x = \frac{12}{2}$

Simplify the right side.

Divide $12$ by $2$ .

$x = 6$