Solve for x 3^(2x-8)=9^(x-4)

$3^{2 x - 8} = 9^{x - 4}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Simplify $2 (x - 4)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $2$ by $- 4$ .

$2 x - 8 = 2 x - 8$

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

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

$2 x - 8 - 2 x = - 8$

Combine the opposite terms in $2 x - 8 - 2 x$ .

Subtract $2 x$ from $2 x$ .

$0 - 8 = - 8$

Subtract $8$ from $0$ .

$- 8 = - 8$

Since $- 8 = - 8$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$