If log₁₀ 2 = 0.3010 and log₁₀ 3 = 0.4771, find the number of digits in the integer 6²⁰.

Model Answer & Options

Source: Extra Practice

15

16

17

18

Explanation

To find the number of digits in a number N, we find log₁₀ N. Here, N = 6²⁰. log₁₀(6²⁰) = 20 * log₁₀(2 * 3) = 20 * (log₁₀ 2 + log₁₀ 3) = 20 * (0.3010 + 0.4771) = 20 * 0.7781 = 15.562. The characteristic is 15. The number of digits is equal to characteristic + 1, which is 15 + 1 = 16. Option B is correct.

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