Solve for x 81^x=243^(x+2)

$81^{x} = 243^{x + 2}$

Step 1

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

$3^{4 x} = 3^{5 (x + 2)}$

Step 2

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

$4 x = 5 (x + 2)$

Step 3

Solve for $x$ .

Simplify $5 (x + 2)$ .

Apply the distributive property.

$4 x = 5 x + 5 \cdot 2$

Multiply $5$ by $2$ .

$4 x = 5 x + 10$

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

Subtract $5 x$ from both sides of the equation.

$4 x - 5 x = 10$

Subtract $5 x$ from $4 x$ .

$- x = 10$

Divide each term in $- x = 10$ by $- 1$ and simplify.

Divide each term in $- x = 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{10}{- 1}$

Divide $x$ by $1$ .

$x = \frac{10}{- 1}$

Simplify the right side.

Divide $10$ by $- 1$ .

$x = - 10$