Precalculus Examples

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

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

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

Step 2

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

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

Step 3

Logarithm base $25$ of $5$ is $\frac{1}{2}$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $2$ .

$\frac{1}{4}$