Precalculus Examples

$\sqrt{125} = 5^{x}$

Step 1

Rewrite the equation as $5^{x} = \sqrt{125}$ .

$5^{x} = \sqrt{125}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{125}$ as $125^{\frac{1}{2}}$ .

$5^{x} = 125^{\frac{1}{2}}$

Step 3

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

$5^{x} = 5^{3 (\frac{1}{2})}$

Step 4

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

$x = 3 (\frac{1}{2})$

Step 5

Combine $3$ and $\frac{1}{2}$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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