Decision Boundary

The decision boundary is $F(x)=\log \left(\frac{P(y=0|x)}{P(y=1|x)}\right)=0$ As we have for the zero level set: $P(y=0|x)=P(y=1|x)$ $\to \log (1)=0$

We can proof this by rewriting the upper formulation to the Logistic Function.