Master Method

I tried to use the Master Method, but I wasn't able to fit the expression to this:

T(n) = a*T(n) + O(n^d)

So I tried to limit the expression this way:

T(n) = 2*T(n/2) + O(log(n))

T'(n) = 2*T(n/2) + O(1)
T''(n) = 2*T(n/2) + O(n)

where T'(n) <= T(n) <= T''(n).

Given by the Master Theorem, O(T'(n)) = O(n) and O(T''(n)) = O(nlog(n)),

O(n) <= T(n) <= O(nlog(n))

Then, according to Master Teorem Case 1, I tried to fix log(n) = O(n^log_2(2-eps):

if eps = 0, O(n^log_2(2-eps)) = O(n), and with eps = 1 it would be O(n^0) = O(1).
So we can figure out that exists a eps between 0 and 1 that it will be O(log(n)),

so finally the expression is O(n).