Evaluate 9^(x-8)=3^(4x-12)

$9^{x - 8} = 3^{4 x - 12}$

Step 1

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

$3^{2 (x - 8)} = 3^{4 x - 12}$

Step 2

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

$2 (x - 8) = 4 x - 12$

Step 3

Solve for $x$ .

Simplify $2 (x - 8)$ .

Rewrite.

$0 + 0 + 2 (x - 8) = 4 x - 12$

Simplify by adding zeros.

$2 (x - 8) = 4 x - 12$

Apply the distributive property.

$2 x + 2 \cdot - 8 = 4 x - 12$

Multiply $2$ by $- 8$ .

$2 x - 16 = 4 x - 12$

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

Subtract $4 x$ from both sides of the equation.

$2 x - 16 - 4 x = - 12$

Subtract $4 x$ from $2 x$ .

$- 2 x - 16 = - 12$

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

Add $16$ to both sides of the equation.

$- 2 x = - 12 + 16$

Add $- 12$ and $16$ .

$- 2 x = 4$

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 $- 2$ .

$x = - 2$