Expand the Logarithmic Expression log of (x cube root of y)/(z^2)

$\log (\frac{x \sqrt[3]{y}}{z^{2}})$

Rewrite $\log (\frac{x \sqrt[3]{y}}{z^{2}})$ as $\log (x \sqrt[3]{y}) - \log (z^{2})$ .

$\log (x \sqrt[3]{y}) - \log (z^{2})$

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

$\log (x y^{\frac{1}{3}}) - \log (z^{2})$

Expand $\log (z^{2})$ by moving $2$ outside the logarithm.

$\log (x y^{\frac{1}{3}}) - (2 \log (z))$

Multiply $2$ by $- 1$ .

$\log (x y^{\frac{1}{3}}) - 2 \log (z)$

Rewrite $\log (x y^{\frac{1}{3}})$ as $\log (x) + \log (y^{\frac{1}{3}})$ .

$\log (x) + \log (y^{\frac{1}{3}}) - 2 \log (z)$

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

$\log (x) + \frac{1}{3} \log (y) - 2 \log (z)$

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

$\log (x) + \frac{\log (y)}{3} - 2 \log (z)$