Expand the Logarithmic Expression log of cube root of xyz

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

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

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

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

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

Rewrite $\log (x \cdot y \cdot z)$ as $\log (x \cdot y) + \log (z)$ .

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

Rewrite $\log (x \cdot y)$ as $\log (x) + \log (y)$ .

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

Apply the distributive property.

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

Simplify.

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

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

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

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

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

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

Expand the Logarithmic Expression log of cube root of x*y*z