Solve for x 3^(x-1)=9^(x+2)

$3^{x - 1} = 9^{x + 2}$

Step 1

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

$3^{x - 1} = 3^{2 (x + 2)}$

Step 2

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

$x - 1 = 2 (x + 2)$

Step 3

Solve for $x$ .

Simplify $2 (x + 2)$ .

Rewrite.

$x - 1 = 0 + 0 + 2 (x + 2)$

Simplify by adding zeros.

$x - 1 = 2 (x + 2)$

Apply the distributive property.

$x - 1 = 2 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$x - 1 = 2 x + 4$

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

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

$x - 1 - 2 x = 4$

Subtract $2 x$ from $x$ .

$- x - 1 = 4$

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

Add $1$ to both sides of the equation.

$- x = 4 + 1$

Add $4$ and $1$ .

$- x = 5$

Divide each term in $- x = 5$ by $- 1$ and simplify.

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x = - 5$