From what I understand saying that if an algorithm is in Θ(log(n!)) then it is in O(n log(n)) is correct, as big-O denotes an upper bound. Would it be also correct to say that if an algorithm is in Θ(log(n!)) then it is in Θ(n log(n))?
By plotting the two growths I can see they are similar but is it correct to say that they are equivalent?