Solve for x 1/2(3)^x=9/2

$\frac{1}{2} {(3)}^{x} = \frac{9}{2}$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot 3^{x}) = 2 (\frac{9}{2})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot 3^{x})$ .

Combine $\frac{1}{2}$ and $3^{x}$ .

$2 \frac{3^{x}}{2} = 2 (\frac{9}{2})$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{3^{x}}{2} = 2 (\frac{9}{2})$

Rewrite the expression.

$3^{x} = 2 (\frac{9}{2})$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{x} = 2 (\frac{9}{2})$

Rewrite the expression.

$3^{x} = 9$

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

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

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

$x = 2$