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

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

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

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

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

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

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

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

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

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

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

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

Simplify each term.

Apply the distributive property.

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

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 \log (x)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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