There is no limit on a large value being considered.
f(n)= n^0.0000001 = n^(10^-7)
g(n)=lg n(base 2)
n= 10^8 f(n)= 1.000001842 , g(n)=26.565
Now, I take n = 10^(10^8)
f(n) = n^(10^-7) = (10^(10^8))^(10^-7) = 10^(10^(8-7)) = 10^10
g(n) = 10^8 log10 2
So, f(n) becomes larger. Thus for any x, we can have an n, where nx becomes larger than log n and stays larger from there on wards for any higher n.