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.

Explore how to simplify the logarithmic expression 1/5 log 4 using logarithmic properties and fractional exponent rules. This step-by-step solution covers key mathematical concepts in logarithms, exponents, and roots, making it suitable for high school students in Grades 9-12.

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