Expand the Logarithmic Expression log base 7 of fourth root of 5w+2

$\log_{7} (\sqrt[4]{5 w + 2})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{5 w + 2}$ as ${(5 w + 2)}^{\frac{1}{4}}$ .

$\log_{7} ({(5 w + 2)}^{\frac{1}{4}})$

Expand $\log_{7} ({(5 w + 2)}^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log_{7} (5 w + 2)$

Combine $\frac{1}{4}$ and $\log_{7} (5 w + 2)$ .

$\frac{\log_{7} (5 w + 2)}{4}$