Trigonometry Examples

$\log (\frac{x^{3}}{\sqrt[3]{y}})$

Step 1

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

$\log (x^{3}) - \log (\sqrt[3]{y})$

Step 2

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

$\log (x^{3}) - \log (y^{\frac{1}{3}})$

Step 3

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

$3 \log (x) - \log (y^{\frac{1}{3}})$

Step 4

Expand $\log (y^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$3 \log (x) - (\frac{1}{3} \log (y))$

Step 5

Combine $\frac{1}{3}$ and $\log (y)$ .

$3 \log (x) - \frac{\log (y)}{3}$