To evaluate $\log 64$ without a calculator, follow these steps:

1. Express 64 as a power of 2: $64 = 2^6$

2. Use the logarithmic property: $\log_b(a^c) = c \cdot \log_b(a)$ Applying this to $\log 64$: $\log 64 = \log(2^6) = 6 \cdot \log 2$

3. Substitute approximate value of $\log 2$: From mathematical reference, $\log 2 \approx 0.301$. Therefore: $\log 64 = 6 \cdot 0.301 = 1.806$

So, the value of $\log 64$ is approximately 1.806.

Let me know if you'd like further clarification or detailed steps on how logarithms work!

Here are some related questions to expand your understanding:

1. How would you calculate $\log 128$ without a calculator?
2. Can you express $\log 64$ in terms of a different base, such as base 10 or base 5?
3. What is the general formula for converting between logarithm bases?
4. Why is $\log_b(a^c) = c \cdot \log_b(a)$ useful in logarithmic calculations?
5. How can you approximate $\log 64$ using mental math or a logarithm table?

Tip: Memorizing common logarithmic values like $\log 2 \approx 0.301$ or $\log 10 = 1$ can save time in calculations.