O(g) = log N
The largest power of N in a polynomial is always its big Oh notation
Any function containing just a logarithm has O(log N).
To find which algorithm is best for which values of N, the simplest way is probably just to solve f(N) = g(N) and then test a number in each interval between the solutions to find out which is better in that interval.
They probably want you to say that it is only useful for large values of N.What does this tell you about using Big OH to decided which algorithm to use?