OJ Board

I don't remember exactly but main idea is to use logs. We're searching x, and there must be

N*10^k <= 2^x and 2^x < (N+1)*10^k, k -- number of missed digits, so
log2(N*10^k) <= log2(2^x) and log2(2^x) < log2((N+1)*10^k)
log2(N) + k*log2(10) <= x and x < log2(N+1) + k*log2(10)

With these ...