Precalculus Examples

$\log_{8} (\frac{x^{6}}{\sqrt[4]{y}})$

Step 1

Rewrite $\log_{8} (\frac{x^{6}}{\sqrt[4]{y}})$ as $\log_{8} (x^{6}) - \log_{8} (\sqrt[4]{y})$ .

$\log_{8} (x^{6}) - \log_{8} (\sqrt[4]{y})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y}$ as $y^{\frac{1}{4}}$ .

$\log_{8} (x^{6}) - \log_{8} (y^{\frac{1}{4}})$

Step 3

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

$6 \log_{8} (x) - \log_{8} (y^{\frac{1}{4}})$

Step 4

Expand $\log_{8} (y^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$6 \log_{8} (x) - (\frac{1}{4} \log_{8} (y))$

Step 5

Combine $\frac{1}{4}$ and $\log_{8} (y)$ .

$6 \log_{8} (x) - \frac{\log_{8} (y)}{4}$