Solve for x square root of 3^x=9

$\sqrt{3^{x}} = 9$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3^{x}}$ as $3^{\frac{x}{2}}$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Solve for $x$ .

Multiply both sides of the equation by $2$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 2 \cdot 2$

Simplify the right side.

Multiply $2$ by $2$ .

$x = 4$