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

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

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

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

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

$2 x = 2 (3 - x)$

Solve for $x$ .

Simplify $2 (3 - x)$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $3$ .

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

Multiply $- 1$ by $2$ .

$2 x = 6 - 2 x$

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

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

$2 x + 2 x = 6$

Add $2 x$ and $2 x$ .

$4 x = 6$

Divide each term in $4 x = 6$ by $4$ and simplify.

Divide each term in $4 x = 6$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4}$

Divide $x$ by $1$ .

$x = \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$x = \frac{2 (3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 3}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 3}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

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

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