Precalculus Examples

$\log_{7} (\frac{x^{3}}{\sqrt[4]{y}})$

Step 1

Rewrite $\log_{7} (\frac{x^{3}}{\sqrt[4]{y}})$ as $\log_{7} (x^{3}) - \log_{7} (\sqrt[4]{y})$ .

$\log_{7} (x^{3}) - \log_{7} (\sqrt[4]{y})$

Step 2

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

$\log_{7} (x^{3}) - \log_{7} (y^{\frac{1}{4}})$

Step 3

Expand $\log_{7} (x^{3})$ by moving $3$ outside the logarithm.

$3 \log_{7} (x) - \log_{7} (y^{\frac{1}{4}})$

Step 4

Expand $\log_{7} (y^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$3 \log_{7} (x) - (\frac{1}{4} \log_{7} (y))$

Step 5

Combine $\frac{1}{4}$ and $\log_{7} (y)$ .

$3 \log_{7} (x) - \frac{\log_{7} (y)}{4}$