Can you find the first digit of $2021^{2021}$ without a computer? Good luck!
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Isn't the methodology basically the same as first digit of 3^2020? – Bubbler Jan 15 '21 at 07:13
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It think the only difference is log(2021) = log (43)+log(47), agreed basically the same. – Oray Jan 15 '21 at 07:26
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The first Google Images hit on "logarithm table" gives the value of log(2.021) just fine. – Bubbler Jan 15 '21 at 07:34
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Wait, the table gives 2021×log(2.021) ~ 2021×0.3056 = 617.6176, which gives the starting digit of 4, but it's incorrect... – Bubbler Jan 15 '21 at 07:46
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@Bubbler It seems that you need at least 5 decimals of accuracy because of that 4-digit factor 2021. – Jaap Scherphuis Jan 15 '21 at 09:55
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2I agree about the closure of this question. I forgot that I already made a similar question. – Dmitry Kamenetsky Jan 15 '21 at 10:00