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.