Total Number of digits

For discussing Olympiad Level Number Theory problems
samiul_samin
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Total Number of digits

Unread post by samiul_samin » Sun Feb 18, 2018 8:54 pm

How many digits in the number $2007^{2007}$
Topic no 3500!!!!!!!

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Zafar
Posts:10
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Location:Dhaka , Bangladesh

Re: Total Number of digits

Unread post by Zafar » Thu Mar 11, 2021 6:51 pm

well ,the number of digits in an exponential number n^k is floor[1+{kln(n)/ln(10)} ]( I don't have proof for this algorithm ) . So I found the solution to be 6629 .

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