Q.Evaluate $\log_4 64$ using the change-of-base formula (change to base 2).

Both 4 and 64 are clean powers of 2, so changing to base 2 makes both parts of the change-of-base formula easy to evaluate directly.

By the change-of-base formula, converting to base $2$:

Evaluate each piece: $2^6=64 \Rightarrow \log_2 64=6$; and $2^2=4 \Rightarrow \log_2 4=2$.

$\log_4 64 = \frac{6}{2} = 3$ …

Inverting the change-of-base fraction (computing $\log_2 4 \div \log_2 64 = 2/6=1/3$ instead of $6/2=3$) — the ARGUMENT's logarithm (64) always goes in the numerator …