Expand the Logarithmic Expression log of (x^2z)/( cube root of y)

$\log (\frac{x^{2} z}{\sqrt[3]{y}})$

Step 1

Rewrite $\log (\frac{x^{2} z}{\sqrt[3]{y}})$ as $\log (x^{2} z) - \log (\sqrt[3]{y})$ .

$\log (x^{2} z) - \log (\sqrt[3]{y})$

Step 2

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

$\log (x^{2} z) - \log (y^{\frac{1}{3}})$

Step 3

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

$\log (x^{2} z) - (\frac{1}{3} \log (y))$

Step 4

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

$\log (x^{2} z) - \frac{\log (y)}{3}$

Step 5

Rewrite $\log (x^{2} z)$ as $\log (x^{2}) + \log (z)$ .

$\log (x^{2}) + \log (z) - \frac{\log (y)}{3}$

Step 6

Expand $\log (x^{2})$ by moving $2$ outside the logarithm.

$2 \log (x) + \log (z) - \frac{\log (y)}{3}$