To simplify the expression \( \frac{1}{5} \log 4 \), we can use the property of logarithms:

\[
a \log_b(x) = \log_b(x^a)
\]

In this case, we have \( a = \frac{1}{5} \) and \( x = 4 \), so:

\[
\frac{1}{5} \log(4) = \log(4^{\frac{1}{5}})
\]

This simplifies to:

\[
\log(4^{\frac{1}{5}}) = \log(\sqrt[5]{4})
\]

Thus, \( \frac{1}{5} \log 4 = \log(\sqrt[5]{4}) \).

If you need the numerical value, I can calculate that for you as well. Would you like to proceed with that?

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Here are some related problems to explore:
1. Simplify \( \frac{1}{3} \log 8 \).
2. Express \( \frac{1}{7} \log 49 \) using logarithmic properties.
3. Solve \( \frac{2}{5} \log 16 \) in a similar manner.
4. Find the exact value of \( \frac{1}{4} \log 81 \).
5. Calculate \( \frac{1}{n} \log x \) for a general \( n \) and \( x \).

**Tip:** Always remember logarithmic properties like \( \log_b(x^a) = a \log_b(x) \), which help simplify logarithmic expressions efficiently.

Explore how to simplify the logarithmic expression 1/5 log 4 using the property a log_b(x) = log_b(x^a). This problem demonstrates key logarithmic concepts and exponentiation, suitable for high school students in Grades 9-12.

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