Q.Evaluate $\log_2 32$.

Evaluating a logarithm means finding the exponent that turns the base into the given number.

Since $2^5=32$, $\log_2 32=5$.

$\log_2 32$ asks: "$2$ raised to what power gives $32$?" Testing successive powers of $2$: $2^1=2,\ 2^2=4,\ 2^3=8,\ 2^4=16,\ 2^5=32$ — a match at the 5th power.

Check (independent recomputation): convert back to exponential form: $2^5=2\times2\times2\times2\times2=32$ ✓, exactly the original number.

Miscounting the number of times $2$ is multiplied by itself to reach $32$ (e.g. wrongly answering $4$ or $6$), especially when working out the powers of 2 mentally without listing them one at a time.