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

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

Step 1

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

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

Step 2

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

$2 x = 1 - x$

Step 3

Solve for $x$ .

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

Add $x$ to both sides of the equation.

$2 x + x = 1$

Add $2 x$ and $x$ .

$3 x = 1$

Divide each term in $3 x = 1$ by $3$ and simplify.

Divide each term in $3 x = 1$ by $3$ .

$\frac{3 x}{3} = \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{1}{3}$

Divide $x$ by $1$ .

$x = \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{3}$

Decimal Form:

$x = 0.\overline{3}$