Precalculus Examples

$\log_{4} (x \cdot \sqrt[6]{y})$

Step 1

Rewrite $\log_{4} (x \cdot \sqrt[6]{y})$ as $\log_{4} (x) + \log_{4} (\sqrt[6]{y})$ .

$\log_{4} (x) + \log_{4} (\sqrt[6]{y})$

Step 2

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

$\log_{4} (x) + \log_{4} (y^{\frac{1}{6}})$

Step 3

Expand $\log_{4} (y^{\frac{1}{6}})$ by moving $\frac{1}{6}$ outside the logarithm.

$\log_{4} (x) + \frac{1}{6} \log_{4} (y)$

Step 4

Combine $\frac{1}{6}$ and $\log_{4} (y)$ .

$\log_{4} (x) + \frac{\log_{4} (y)}{6}$