The product rule for logarithms states that:
$$\log_b M + \log_b N = \log_b (M\cdot N)$$
Most sources that I've found* state that this rule only applies when $M$ and $N$ are positive. It's true that $\log_b 0$ is undefined, but negative values in place of $M$ and $N$ seem to work just fine:
$$\log(-1) + \log(4) = \log(-1\cdot 4)$$
Why the discrepancy?