How many digits are there in 2^64?

Introduction / Context:Digit count uses base-10 logarithms: digits = floor(log10 N) + 1 for positive integers N. We are given N = 2^64, so we only need log10 2 and multiplication.

Given Data / Assumptions:

• N = 2^64.
• Use log10 2 ≈ 0.30103 (common value).

Concept / Approach:

• Compute log10 N = 64 × log10 2.
• Apply digits = floor(log10 N) + 1.

Step-by-Step Solution:

Verification / Alternative check:2^10 ≈ 10^3, so 2^60 ≈ 10^18; multiply by 2^4 = 16 gives about 1.6 × 10^19 ⇒ 20 digits.

Why Other Options Are Wrong:

• 18 or 19 underestimate; 21 overestimates the power.

Final Answer:20 digit