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

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

Step 1

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

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

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y^{4}}$ as $y^{\frac{4}{3}}$ .

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

Step 3

Rewrite $\log (y^{\frac{4}{3}} z^{4})$ as $\log (y^{\frac{4}{3}}) + \log (z^{4})$ .

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

Step 4

Expand $\log (y^{\frac{4}{3}})$ by moving $\frac{4}{3}$ outside the logarithm.

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

Step 5

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

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

Step 6

Combine $\frac{4}{3}$ and $\log (y)$ .

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