Solve for x 9^(4x)=81^(x+2)

$9^{4 x} = 81^{x + 2}$

Step 1

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

$9^{4 x} = 9^{2 (x + 2)}$

Step 2

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

$4 x = 2 (x + 2)$

Step 3

Solve for $x$ .

Simplify $2 (x + 2)$ .

Apply the distributive property.

$4 x = 2 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$4 x = 2 x + 4$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$4 x - 2 x = 4$

Subtract $2 x$ from $4 x$ .

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$