Algebra Examples

$\log_{\sqrt{a}} (a^{2})$

Step 1

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

$\log_{a^{\frac{1}{2}}} (a^{2})$

Step 2

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

$2 \log_{a^{\frac{1}{2}}} (a)$