In decimal representation find the largest N-digit number which is an N-th power.

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