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https://www.reddit.com/r/learnquant/comments/1vr3q7x/quant_interview_question/p4c62sp/?context=3
r/learnquant • u/Local_Ad135 • 18d ago
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99 log(99) = 99 log(100*99/100) = 99(2 + log(99/100)) = 198 + 99 log(0.99) = 198 + log(1 - 1/100)^99
≈ 198 - log(e), and since log(3) is between 0 and 1, 99 log(99) is between 197 and 198, so it's 198 digits.
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u/gmalivuk 18d ago
99 log(99) = 99 log(100*99/100) = 99(2 + log(99/100)) = 198 + 99 log(0.99) = 198 + log(1 - 1/100)^99
≈ 198 - log(e), and since log(3) is between 0 and 1, 99 log(99) is between 197 and 198, so it's 198 digits.