Precalculus Examples

$\log_{0.2} (\sqrt{5})$

Step 1

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

$\log_{0.2} (5^{\frac{1}{2}})$

Step 2

Expand $\log_{0.2} (5^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{0.2} (5)$

Step 3

Combine $\frac{1}{2}$ and $\log_{0.2} (5)$ .

$\frac{\log_{0.2} (5)}{2}$