Master theorem. Particular example I can't understand

Question

I thought that I understood how to use the Master Theorem but apparently I don't. So here it is:

     T(n) = 16 T(n/2) +2(n^4)
     T(n) = aT(n/b) + f(n^c)
     a=16 
     b=2
     log base b of a = log base 2 of 16 = 4 
     c = 4 

c and log base b of a are equal to each other, I think that this is the 2nd case of the master theorem. So big Theta should be (n^4 log n) but everybody says it's n^4.

I can't understand where I've gone wrong. Could somebody please explain it to me.

Answer 1

You are correct. Using the Master Theorem , $\frac{\log_{2}\left(16\right)}{\log_{2}\left(2\right)}=4=c$ thus $T(n) = \Theta(f(n) \log n)$. Therefore $T(n) = \Theta(n^4 \log n)$.