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The problem asks to evaluate \( \log_4 32 \).

### Solution:

The logarithmic equation \( \log_4 32 = x \) can be rewritten as:
\[
4^x = 32
\]

Now express 32 as a power of 4. We know that \( 32 = 2^5 \), and \( 4 = 2^2 \). Thus:
\[
4^x = (2^2)^x = 2^{2x}
\]
and
\[
2^{2x} = 2^5
\]

Equating the exponents:
\[
2x = 5
\]

Solve for \( x \):
\[
x = \frac{5}{2}
\]

Thus:
\[
\log_4 32 = \frac{5}{2}
\]

### Final Answer:
\[
\log_4 32 = \frac{5}{2}
\]

Would you like further explanation on logarithms or properties of exponents?  

Here are some related questions for practice:
1. Evaluate \( \log_2 64 \).
2. Simplify \( \log_5 25 \).
3. Solve \( \log_3 81 = x \).
4. Convert \( \log_{10} 1000 \) to exponential form.
5. What is the value of \( \log_8 16 \)?

**Tip:** When solving logarithms, always check if the argument (e.g., 32 in this case) can be expressed as a power of the base.

Learn how to evaluate log_4(32) using properties of logarithms and exponents. This step-by-step guide walks through the process of solving 4^x = 32 and expressing 32 as a power of 4. Suitable for high school students.

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