I know that f(n) = O(g(n)) means : 0 < f(n) <= c*g(n) such that c>0, n0>0 and for any n>= n0
but what does f(n) ∈ O(g(n)) mean? I’ve been given an example to solve: f(n) = 3log(n), g(n) = 9^n, f(n) ∈ O(g(n))

Could someone simply explain the meaning of f(n) ∈ O(g(n)) in this case, because I have no idea what I’m supposed to be solving for.

Not at all, there is a great portion of computer science that is owed to the background of mathematical theory and it is the heart of algorithmic complexity calculations. The reality of computer science is just that we cannot really express all algorithms in functional terms so we often end up in the world of approximations (hence why this is an engineering discipline rather than a theoretical / academic discipline).