Precalculus Examples

$\log_{5} (\sqrt{25})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25}$ as $25^{\frac{1}{2}}$ .

$\log_{5} (25^{\frac{1}{2}})$

Step 2

Expand $\log_{5} (25^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{5} (25)$

Step 3

Logarithm base $5$ of $25$ is $2$ .

$\frac{1}{2} \cdot 2$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$\frac{1}{2} \cdot 2$

Step 4.2

Rewrite the expression.

$1$