Expand the Logarithmic Expression log of cube root of 7x^4

$\log (\sqrt[3]{7 x^{4}})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{7 x^{4}}$ as ${(7 x^{4})}^{\frac{1}{3}}$ .

$\log ({(7 x^{4})}^{\frac{1}{3}})$

Expand $\log ({(7 x^{4})}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log (7 x^{4})$

Rewrite $\log (7 x^{4})$ as $\log (7) + \log (x^{4})$ .

$\frac{1}{3} (\log (7) + \log (x^{4}))$

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

$\frac{1}{3} (\log (7) + 4 \log (x))$

Apply the distributive property.

$\frac{1}{3} \log (7) + \frac{1}{3} (4 \log (x))$

Combine $\frac{1}{3}$ and $\log (7)$ .

$\frac{\log (7)}{3} + \frac{1}{3} (4 \log (x))$

Multiply $\frac{1}{3} (4 \log (x))$ .

Combine $4$ and $\frac{1}{3}$ .

$\frac{\log (7)}{3} + \frac{4}{3} \log (x)$

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

$\frac{\log (7)}{3} + \frac{4 \log (x)}{3}$