Solve for x (16)^4=2^((1/2)x)

${(16)}^{4} = 2^{(\frac{1}{2}) x}$

Step 1

Rewrite the equation as $2^{(\frac{1}{2}) x} = 16^{4}$ .

$2^{(\frac{1}{2}) x} = 16^{4}$

Step 2

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

$2^{(\frac{1}{2}) x} = 2^{4 \cdot 4}$

Step 3

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

$(\frac{1}{2}) x = 4 \cdot 4$

Step 4

Solve for $x$ .

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x) = 2 (4 \cdot 4)$

Simplify both sides of the equation.

Simplify the left side.

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 2 (4 \cdot 4)$

Simplify the right side.

Multiply $2 (4 \cdot 4)$ .

Multiply $4$ by $4$ .

$x = 2 \cdot 16$

Multiply $2$ by $16$ .

$x = 32$