Algorithms recurrence equation using unwinding / substitution

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This is homework for introduction to Algorithms this is what I have below.

  1. (25 pts) Use the direct unwinding to prove that the recurrence equation T(n)= 2T(n/2)+ nlogn has a lower bound of (nlogn). Hint: It is essentially to prove that T(n) = BigOmegaK(nlogn).

This is what I have I am just confused on the last part I belive my unwinding is correct.

T(n) = 2T(n/2) + nlogn

 = 4T(n/4) + nlog(n/2) + nlogn

 = 8T(n/8) + nlog(n/4) + nlog(n/2) + nlogn

I am not sure how to prove a lower bound of nlogn?