## Complexity of the following function $f(n) = 1000+\log_{2}(n^{9n})+3n\log_{1000}(n^{n})$

I know that $$f(n) = 1000+\log_{2}(n^{9n})+3n\log_{1000}(n^{n}) \in O(n^2\log{n})$$, but how can you derive this. I mean you choose the strongest increasing term with the $$n$$ in it and then you remove all the constants and that is you complexity but I do not know how to derive the above function. Can someone help me out?