Precalculus Examples

$\log_{8} (\sqrt[6]{29})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[6]{29}$ as $29^{\frac{1}{6}}$ .

$\log_{8} (29^{\frac{1}{6}})$

Step 2

Expand $\log_{8} (29^{\frac{1}{6}})$ by moving $\frac{1}{6}$ outside the logarithm.

$\frac{1}{6} \log_{8} (29)$

Step 3

Combine $\frac{1}{6}$ and $\log_{8} (29)$ .

$\frac{\log_{8} (29)}{6}$