How-many-digits-doest-the-number-2021-2022-have-

Question Number 144609 by mathdanisur last updated on 26/Jun/21

H o w m a n y d i g i t s d o e s t t h e n u m b e r

2021^{2022} h a v e . ?

Answered by MJS_new last updated on 27/Jun/21

\log_{10} 2021^{2022} = {2022 \log}_{10} 2021 =

= {2022 \log}_{10} (2.021 \times 10^{3}) = 2022 (3 + \log_{10} 2.021) =

= 6066 + {2022 \log}_{10} 2.021 \approx 6683.85508593 \approx

\approx 7.16285117718 \times 10^{6683} which has 6684 digits

Commented by mathdanisur last updated on 27/Jun/21

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