If log 2 = 0.30103, the number of digits in 264 is:

Concept: For a positive integer N, if log10 N = n + f, where n is a non-negative integer (the characteristic) and 0 ≤ f < 1 (the mantissa), then N has exactly n + 1 digits.

1. Write log10(264) = 64 × log102, using the power rule of logarithms.

2. Substitute log102 = 0.30103: 64 × 0.30103 = 19.26592.

3. The characteristic (integer part) of 19.26592 is 19, so the number of digits = 19 + 1 = 20.

Cross-check: 210 = 1024 ≈ 103.01, so 264 = (210)6.4 ≈ 1019.26, consistent with the result above. Indeed, 264 = 18,446,744,073,709,551,616, which has 20 digits, confirming the answer.