Solve for x 9^(3x-2)=27^(2x-2)

$9^{3 x - 2} = 27^{2 x - 2}$

Step 1

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

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

Step 2

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

$2 (3 x - 2) = 3 (2 x - 2)$

Step 3

Solve for $x$ .

Simplify $2 (3 x - 2)$ .

Rewrite.

$0 + 0 + 2 (3 x - 2) = 3 (2 x - 2)$

Simplify by adding zeros.

$2 (3 x - 2) = 3 (2 x - 2)$

Apply the distributive property.

$2 (3 x) + 2 \cdot - 2 = 3 (2 x - 2)$

Multiply.

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 2 = 3 (2 x - 2)$

Multiply $2$ by $- 2$ .

$6 x - 4 = 3 (2 x - 2)$

Simplify $3 (2 x - 2)$ .

Apply the distributive property.

$6 x - 4 = 3 (2 x) + 3 \cdot - 2$

Multiply.

Multiply $2$ by $3$ .

$6 x - 4 = 6 x + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$6 x - 4 = 6 x - 6$

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

Subtract $6 x$ from both sides of the equation.

$6 x - 4 - 6 x = - 6$

Combine the opposite terms in $6 x - 4 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 4 = - 6$

Subtract $4$ from $0$ .

$- 4 = - 6$

Since $- 4 \neq - 6$ , there are no solutions.

No solution