Alright, in order to show that a specific funtion is (theta) some other function, we have to check the big-O and Omega notations first.
In other words..
If we have f(n) = n - 27 as our function and we need to show whether f(n) is theta (log n) for instance. Then first we have to show that f(n) is omega (log n) and f(n) is big-o (log n) at the same time. If those two derivations apply to the fucntion then we can say that f(n) IS theta (log n).
If one of them fails then f(n) is not theta (log n).
I'm not sure if it makes sense to you here or even if this what you mean by your question. The question is not clear.. whats the fucntion that were supposed to be basing our first fucntion(the one you mentioned) on ??