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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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