2020 · Q3
How many digits are there in (54)^10? (Given that log₁₀2 = 0.301 and log₁₀3 = 0.477)
Elementary MathematicsNumber System
- A16
- B18
- C19
- D27
Explanation
The number of digits of N is ⌊log₁₀N⌋ + 1. Here log₁₀(54¹⁰) = 10·log₁₀(2×3³) = 10(0.301 + 3×0.477) = 10(1.732) = 17.32. The integer part is 17, so (54)¹⁰ has 17 + 1 = 18 digits.