Precalculus Examples

$\log_{6} (\frac{y^{5}}{\sqrt[3]{x}})$

Step 1

Rewrite $\log_{6} (\frac{y^{5}}{\sqrt[3]{x}})$ as $\log_{6} (y^{5}) - \log_{6} (\sqrt[3]{x})$ .

$\log_{6} (y^{5}) - \log_{6} (\sqrt[3]{x})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$\log_{6} (y^{5}) - \log_{6} (x^{\frac{1}{3}})$

Step 3

Expand $\log_{6} (y^{5})$ by moving $5$ outside the logarithm.

$5 \log_{6} (y) - \log_{6} (x^{\frac{1}{3}})$

Step 4

Expand $\log_{6} (x^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$5 \log_{6} (y) - (\frac{1}{3} \log_{6} (x))$

Step 5

Combine $\frac{1}{3}$ and $\log_{6} (x)$ .

$5 \log_{6} (y) - \frac{\log_{6} (x)}{3}$