n
and log n
are not asymptotically equal. If you try to calculate lim n / log n
in n = inf
limit, you can use L'Hôpital's rule and end up quickly with lim n
which is infinity, thus proving that n
is assymptotically bigger than log n
.
However, the bigger problem is that, according to few places your problem is ill-conditioned. This case does not satisfy the preconditions for the Master Theorem. Loot at Example 7. - exactly your case.