Expand the Logarithmic Expression log of ( cube root of y^4z)/(x^2)

$\log (\frac{\sqrt[3]{y^{4}} z}{x^{2}})$

Rewrite $\log (\frac{\sqrt[3]{y^{4}} z}{x^{2}})$ as $\log (\sqrt[3]{y^{4}} z) - \log (x^{2})$ .

$\log (\sqrt[3]{y^{4}} z) - \log (x^{2})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y^{4}}$ as $y^{\frac{4}{3}}$ .

$\log (y^{\frac{4}{3}} z) - \log (x^{2})$

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

$\log (y^{\frac{4}{3}} z) - (2 \log (x))$

Multiply $2$ by $- 1$ .

$\log (y^{\frac{4}{3}} z) - 2 \log (x)$

Rewrite $\log (y^{\frac{4}{3}} z)$ as $\log (y^{\frac{4}{3}}) + \log (z)$ .

$\log (y^{\frac{4}{3}}) + \log (z) - 2 \log (x)$

Expand $\log (y^{\frac{4}{3}})$ by moving $\frac{4}{3}$ outside the logarithm.

$\frac{4}{3} \log (y) + \log (z) - 2 \log (x)$

Combine $\frac{4}{3}$ and $\log (y)$ .

$\frac{4 \log (y)}{3} + \log (z) - 2 \log (x)$