Condense the expression $3\log_7v+6\log_7w-\frac{\log_7u}{3}$

Question

I am to condense the expression $3\log_7v+6log_7w-\frac{\log_7u}{3}$. The solution is provided as $\log_7(\frac{v^3w^6}{\sqrt[3]{u}})$

I can see how the numerator was arrived at using the properties of logs but I cannot see how the denominator is obtained?

As far as I got:

$log_7(\frac{v^3w^6}{\frac{\log_7u}{3}})$

In baby steps, how can I get my denominator from $\frac{\log_7u}{3}$ to $\sqrt[3]{u}$

Answer 1

$$3\log_7v+6\log_7w-\frac{\log_7u}{3} = \log_7v^3 + \log_7w^6 - \log_7u^{1/3} = \log_7(\frac {v^3w^6}{u^{1/3}}).$$

Is that clear now?