Algebra Examples

$8^{x - 2} = \sqrt{8}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8}$ as $8^{\frac{1}{2}}$ .

$8^{x - 2} = 8^{\frac{1}{2}}$

Step 2

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

$x - 2 = \frac{1}{2}$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $2$ to both sides of the equation.

$x = \frac{1}{2} + 2$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{1}{2} + 2 \cdot \frac{2}{2}$

Step 3.3

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

$x = \frac{1}{2} + \frac{2 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$x = \frac{1 + 2 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $2$ .

$x = \frac{1 + 4}{2}$

Step 3.5.2

Add $1$ and $4$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.5$

Mixed Number Form:

$x = 2 \frac{1}{2}$