Expand the Logarithmic Expression log of (y^4z)/( cube root of x^2)

$\log (\frac{y^{4} z}{\sqrt[3]{x^{2}}})$

Step 1

Rewrite $\log (\frac{y^{4} z}{\sqrt[3]{x^{2}}})$ as $\log (y^{4} z) - \log (\sqrt[3]{x^{2}})$ .

$\log (y^{4} z) - \log (\sqrt[3]{x^{2}})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2}}$ as $x^{\frac{2}{3}}$ .

$\log (y^{4} z) - \log (x^{\frac{2}{3}})$

Step 3

Expand $\log (x^{\frac{2}{3}})$ by moving $\frac{2}{3}$ outside the logarithm.

$\log (y^{4} z) - (\frac{2}{3} \log (x))$

Step 4

Combine $\frac{2}{3}$ and $\log (x)$ .

$\log (y^{4} z) - \frac{2 \log (x)}{3}$

Step 5

Rewrite $\log (y^{4} z)$ as $\log (y^{4}) + \log (z)$ .

$\log (y^{4}) + \log (z) - \frac{2 \log (x)}{3}$

Step 6

Expand $\log (y^{4})$ by moving $4$ outside the logarithm.

$4 \log (y) + \log (z) - \frac{2 \log (x)}{3}$