Solve for x 81^(3x-3)=729^(x+2)

$81^{3 x - 3} = 729^{x + 2}$

Step 1

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

$9^{2 (3 x - 3)} = 9^{3 (x + 2)}$

Step 2

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

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

Step 3

Solve for $x$ .

Simplify $2 (3 x - 3)$ .

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $2$ .

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

Multiply $2$ by $- 3$ .

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

Simplify $3 (x + 2)$ .

Apply the distributive property.

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

Multiply $3$ by $2$ .

$6 x - 6 = 3 x + 6$

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

Subtract $3 x$ from both sides of the equation.

$6 x - 6 - 3 x = 6$

Subtract $3 x$ from $6 x$ .

$3 x - 6 = 6$

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

Add $6$ to both sides of the equation.

$3 x = 6 + 6$

Add $6$ and $6$ .

$3 x = 12$

Divide each term in $3 x = 12$ by $3$ and simplify.

Divide each term in $3 x = 12$ by $3$ .

$\frac{3 x}{3} = \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{12}{3}$

Divide $x$ by $1$ .

$x = \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x = 4$

Solve for x 81^(3x-3)=729^(x+2)

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