Expand the Logarithmic Expression log of (x^5z)/( cube root of y^4)

$\log (\frac{x^{5} z}{\sqrt[3]{y^{4}}})$

Rewrite $\log (\frac{x^{5} z}{\sqrt[3]{y^{4}}})$ as $\log (x^{5} z) - \log (\sqrt[3]{y^{4}})$ .

$\log (x^{5} z) - \log (\sqrt[3]{y^{4}})$

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

$\log (x^{5} z) - \log (y^{\frac{4}{3}})$

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

$\log (x^{5} z) - (\frac{4}{3} \log (y))$

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

$\log (x^{5} z) - \frac{4 \log (y)}{3}$

Rewrite $\log (x^{5} z)$ as $\log (x^{5}) + \log (z)$ .

$\log (x^{5}) + \log (z) - \frac{4 \log (y)}{3}$

Expand $\log (x^{5})$ by moving $5$ outside the logarithm.

$5 \log (x) + \log (z) - \frac{4 \log (y)}{3}$