I was reviewing the main theorem of https://brilliant.org/wiki/master-theorem/ and I was trying to solve a question.

Which of the following factors increases more rapidly asymptotically?

(a) $ T (n) = 4T (n / 2) + 10n $

(B) $ T (n) = 8T (n / 3) + 24n ^ 2 $

(C) $ T (n) = 16T (n / 4) + 10n ^ 2 $

(re) $ T (n) = 25T (n / 5) + 20 (nlogn) ^ {1.99} $

e) They are all asymptotically identical

My calculation says, (a) is $ theta (n ^ 2) $ (b) is $ theta (n ^ 2) $ (it is $ theta (n ^ 2logn) $. Now, how can I evaluate (d)?

Yes $ f (n) $ is smaller or bigger than $ n ^ {log_b a} $by less than a polynomial factor, how can I solve T (n)?