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If log(2) = 0.3010, the number of digits in 5^20 is
A16
B13
C14
D15
Answer & Solution
Correct answer: C. 14
1. Number of digits = floor(log10(N)) + 1.
2. log10(5^20) = 20 * log10(5) = 20 * log10(10/2) = 20 * (1 - 0.3010) = 20 * 0.6990 = 13.980.
3. floor(13.980) + 1 = 13 + 1 = 14.
4. So 5^20 has 14 digits.
_Source: ICAI BoS Foundation Paper 3, Ch 1 Unit IV 'Logarithms', p.19_
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