Final answer:
The Master theorem cannot be directly applied to solve the recurrence relation T(n) = 2T(n/2) + n/logn because it does not neatly fall into any of the standard cases, particularly because of the n/logn term.
Step-by-step explanation:
The question is asking to solve the recurrence relation T(n) = 2T(n/2) + n/logn using the Master theorem. To apply the Master theorem, we usually look for recurrences of the form T(n) = aT(n/b) + f(n), where a ≥ 1 and b > 1 are constants, and f(n) is an asymptotically positive function. However, the presence of n/logn complicates direct application of the standard form of the Master theorem, as the theorem typically addresses polynomials of n, not functions involving logarithms.
Hence, while we can try to compare n/logn to n^log_b(a) to find the typical cases of the theorem, this particular recurrence does not fit neatly into any of the cases because the Master theorem does not directly cover situations where the additional term involves a division by a logarithm. In order to solve this recurrence relation, one might have to rely on more advanced techniques in analysis of algorithms or look for specialized extensions of the Master theorem that can address the logarithmic term involved.