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

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

Step 1

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

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

Step 2

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

$3 x = 2 (2 - x)$

Step 3

Solve for $x$ .

Simplify $2 (2 - x)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $2$ .

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

Multiply $- 1$ by $2$ .

$3 x = 4 - 2 x$

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

Add $2 x$ to both sides of the equation.

$3 x + 2 x = 4$

Add $3 x$ and $2 x$ .

$5 x = 4$

Divide each term in $5 x = 4$ by $5$ and simplify.

Divide each term in $5 x = 4$ by $5$ .

$\frac{5 x}{5} = \frac{4}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{4}{5}$

Divide $x$ by $1$ .

$x = \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{5}$

Decimal Form:

$x = 0.8$