Explanation

The number of digits of N is ⌊log₁₀ N⌋ + 1. Here log₁₀(2⁴⁰) = 40 × log₁₀ 2 = 40 × 0.301 = 12.04. So 2⁴⁰ has ⌊12.04⌋ + 1 = 13 digits: option B. Option A (14) wrongly rounds 12.04 up instead of taking the floor.