The expression $\frac{1}{5} \log 4$ can be simplified as follows:

1. Use the logarithmic property: $a \log b = \log b^a$ Here, the expression $\frac{1}{5} \log 4$ can be rewritten as: $\log 4^{\frac{1}{5}} = \log \left( 4^{1/5} \right)$

2. Simplify $4^{\frac{1}{5}}$, which is the 5th root of 4.

So, the simplified form of $\frac{1}{5} \log 4$ is: $\log \left( \sqrt[5]{4} \right)$

Would you like to explore more details or need any further clarification?

Here are five related questions to expand on this:

1. What are the basic logarithmic properties?
2. How do you calculate fractional exponents like $4^{1/5}$?
3. Can you simplify the logarithm for different bases?
4. What is the relationship between logarithms and exponents?
5. How do you solve logarithmic equations?

Tip: Logarithmic properties can greatly simplify expressions involving powers and roots.