Expand the Logarithmic Expression log base 6 of fourth root of 7x

$\log_{6} (\sqrt[4]{7 x})$

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

$\log_{6} ({(7 x)}^{\frac{1}{4}})$

Expand $\log_{6} ({(7 x)}^{\frac{1}{4}})$ by moving $\frac{1}{4}$ outside the logarithm.

$\frac{1}{4} \log_{6} (7 x)$

Rewrite $\log_{6} (7 x)$ as $\log_{6} (7) + \log_{6} (x)$ .

$\frac{1}{4} (\log_{6} (7) + \log_{6} (x))$

Apply the distributive property.

$\frac{1}{4} \log_{6} (7) + \frac{1}{4} \log_{6} (x)$

Combine $\frac{1}{4}$ and $\log_{6} (7)$ .

$\frac{\log_{6} (7)}{4} + \frac{1}{4} \log_{6} (x)$

Combine $\frac{1}{4}$ and $\log_{6} (x)$ .

$\frac{\log_{6} (7)}{4} + \frac{\log_{6} (x)}{4}$