Precalculus Examples

$\log (\sqrt{5 a^{6} + 1})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 a^{6} + 1}$ as ${(5 a^{6} + 1)}^{\frac{1}{2}}$ .

$\log ({(5 a^{6} + 1)}^{\frac{1}{2}})$

Step 2

Expand $\log ({(5 a^{6} + 1)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (5 a^{6} + 1)$

Step 3

Combine $\frac{1}{2}$ and $\log (5 a^{6} + 1)$ .

$\frac{\log (5 a^{6} + 1)}{2}$