Given log₁₀2 = 0.30103, find the number of digits in 2⁶⁴.

Concept / Approach

• The number of digits of a positive integer N in base 10 is ⌊log₁₀N⌋ + 1.

Step-by-step calculationlog₁₀(2⁶⁴) = 64 × log₁₀2 = 64 × 0.30103 = 19.26592Digits = ⌊19.26592⌋ + 1 = 19 + 1 = 20

Common pitfalls

• Rounding 19.26592 before taking the floor. Always floor first, then add 1.

Final Answer20