Expand the Logarithmic Expression log of (z cube root of x)/(y^3)

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

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

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

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

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

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

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

Multiply $3$ by $- 1$ .

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

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

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

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

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

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

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