Using Induction to prove that $n^3log^4n=O(n^4)$
You showed that f (n) = o (g (n)). That's it. There is nothing else to prove. 

If you look at the definition of o (f (n)) and O (f (n)), they are almost identical except one says "for every eps > 0" and the other says "there is one c > 0". You can take every single eps of the little-o definition and use it as the c in the big-O definition.