let $P0,P1 \leq0$ $s.t$ $P0+P1=1$ (I am not sure if this assumption is required to prove the following equality. But for my application this holds). How does following hold true
\begin{equation} e^{\log(\frac{P1}{P0}+1)}=1+e^{\log(\frac{P1}{P0})} \end{equation}
And how can this be generalized for $n$ positive real numbers $s.t$ $P0+P1+…+Pn=1$ where $Px\leq0$ for $x=1:n$