First k digits of n^n

It is related to problem :http://www.codechef.com/problems/MARCHA4 where we are supposed to find first and last k digits of n^n. To find first k digits i have seen people using some log and floor functions..complete code is below:

long int firstKdigits(long long n,int k)

{ long double x, y;

x = n*log10(n);

y = floor(pow(10,x-floor(x) +k-1));

return ((int)y);

}

Can someone provide me proof of this..how it gives first k digits??