Decision Boundary

The decision boundary is

F(x)=log⁡(P(y=0∣x)P(y=1∣x))=0F(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)P(y=0|x) = P(y=1|x) →log⁡(1)=0\to \log(1)=0

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