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It is not 8^5 (Posted on 2015-06-24) Difficulty: 2 of 5
In decimal representation find the largest N-digit number which is an N-th power.

See The Solution Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution Solution (Spoiler) | Comment 1 of 3

Let x be the number to be raised to some power. Working in base 10:

If x=10, then x^n has (n+1) digits. So x<10.

Let x=9, then log (10^(n-1)) = log (9^n), n=21.845..., so the largest such number is 9^21.


Edited on June 24, 2015, 8:58 am
  Posted by broll on 2015-06-24 08:45:20

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