Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Simplify.

Tap for more steps...

Step 3.1.1

Multiply $2$ by $2$ .

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

Step 3.1.2

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

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

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

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.2.3.2

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

Tap for more steps...

Step 3.2.3.2.1

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

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

Step 3.2.3.2.2

Multiply $2$ by $4$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.625$