Let $\Omega$ be a pseudo convex domain. Let $r$ be any $C^2$ function $r: \mathbb C^2\to \mathbb R$. Let $\Omega: \{z: r(z)<0\}$. Then we know that $\psi: -log(-r)+\lambda |z|^2$ is a plurisubharmonic function for large $\lambda$.

Is $-log(-r)$ also plurisubharmonic? May I have an answer or even a hint? Thanks in advance.