Convert between log base 2 and base 10 in your head. What's log2(10)?

How to answer

From 2^10 ≈ 10^3, take log2: 10 ≈ 3·log2(10), so log2(10) ≈ 10/3 ≈ 3.32 (exact 3.3219); equivalently log10(2) ≈ 0.301. log2(N) = log10(N)×3.32; log10(N) = log2(N)/3.32. These two constants cover almost all log conversions.

Key idea: Confusing the direction: bits = digits × 3.32 (MORE bits than digits). Sanity-check: a 3-digit number needs ~10 bits.