The expression $\frac{1}{5} \log 4$ can be simplified by using logarithmic properties. Here's the step-by-step breakdown:

Step 1: Use the power rule of logarithms

The power rule states that:

$a \log b = \log b^a$

Applying this to your expression:

$\frac{1}{5} \log 4 = \log 4^{\frac{1}{5}}$

Step 2: Simplify the exponent

Simplify the expression $4^{\frac{1}{5}}$:

$4^{\frac{1}{5}} = (2^2)^{\frac{1}{5}} = 2^{\frac{2}{5}}$

So, the expression becomes:

$\frac{1}{5} \log 4 = \log 2^{\frac{2}{5}}$