Solve for x 16^(x/2)=64

$16^{\frac{x}{2}} = 64$

Step 1

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

$4^{2 \frac{x}{2}} = 4^{3}$

Step 2

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

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

Step 3

Solve for $x$ .

Combine $2$ and $\frac{x}{2}$ .

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

Divide each term in $\frac{2 x}{2} = 3$ by $2$ and simplify.

Divide each term in $\frac{2 x}{2} = 3$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = 3$