Let $C$ be the convex subset of $\mathbb{R}^2$ defined by: \begin{align} C = \{(x,y):~~ \log(x) + \log(y) \geq 1;~~ x\geq 0;~~ y\geq 0\} \end{align}
According to the hyperplane separation theorem, if a point $(x_0,y_0)$ is not in $C$, then there is a hyperplane separating $(x_0,y_0)$ from $C$.
MY QUESTION: Given a point $(x_0,y_0)$ with $\log(x_0) + \log(y_0) < 1$, how can I find a hyperplane separating $(x_0,y_0)$ from $C$?