Big Oh and Big Omega when $n$ and $\log n$ terms are in $f(n)$
You are right that you cannot a priori ignore additional terms, although morally you can as the &quot;smaller&quot; terms do not contribute to the asymptotic growth.
As an example $f(n) :=n+\log n$ is in $\Theta(n)$. Why? Going back to the definition, we want to show that $f(n)$ is in $O(n)$ and in $\Omega(n)$. Showing $f(n)\in \Omega(n)$ is immediate, as $f(n) \geq n$ for all $n&gt;0$.
To show that $f(n)$ is in $O(n)$, simply notice that for large enough $n$ (say $n&gt;N$ for some constant $N$) we have $\log n \leq n$ and thus $f(n)\leq 2n$ for all $n&gt;N$. By definition $f(n)\in O(n)$.