Question

Anyone good with logarithms?

Answer 1

I'll give it a shot.
What's the problem?

Answer 2

\[\log_{4} \sqrt[3]{\frac{ X ^{2} }{ Y }}\]

Answer 3

Remember that \( \large\sqrt[n]{a} = a^{ \frac{1}{n} } \)

With that you can rewrite \(\large \sqrt[3]{\frac{ X ^{2} }{ Y }} \) with the root changed into an exponent.

Then remember two rules of exponents:

\(\large \log a^n = n \log a\)

and

\(\large \log \dfrac{a}{b} = \log a - \log b \)

Use the first rule of exponents to take care of the exponent 1/3.
Then use the second rule to deal with the fraction.
Then use the first rule again to deal with the exponent 2.