Solve for x 4^(2x)=32^(1/2)

$4^{2 x} = 32^{\frac{1}{2}}$

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

$2^{2 (2 x)} = 2^{5 (\frac{1}{2})}$

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

$2 (2 x) = 5 (\frac{1}{2})$

Solve for $x$ .

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Simplify.

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Multiply $2$ by $2$ .

$4 x = 5 (\frac{1}{2})$

Combine $5$ and $\frac{1}{2}$ .

$4 x = \frac{5}{2}$

Divide each term by $4$ and simplify.

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Divide each term in $4 x = \frac{5}{2}$ by $4$ .

$\frac{4 x}{4} = \frac{5}{2} \cdot \frac{1}{4}$

Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4 x}{4} = \frac{5}{2} \cdot \frac{1}{4}$

Divide $x$ by $1$ .

$x = \frac{5}{2} \cdot \frac{1}{4}$

Multiply $\frac{5}{2} \cdot \frac{1}{4}$ .

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Multiply $\frac{5}{2}$ and $\frac{1}{4}$ .

$x = \frac{5}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{5}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{8}$

Decimal Form:

$x = 0.625$

Solve for x 4^(2x)=32^(1/2)

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