I am a physics graduate and trying to understand one of the assumptions made for isochron dating of rocks: at crystallization time of the rock, $t=0$, the ratio of the parent isotope to a stable reference daughter isotope was variable for different parts/minerals of the rock ($P/D_{ref}\neq const$), but the ratio of the radiogenic daughter isotope to the stable reference daughter isotope was constant ($D*/D_{ref}=const$). See for that the figure below taken from here :
My question: Why is the one ratio constant, but the other not? I taught $D*/D_{ref}=const$ holds, because just before $t=0$ the rock is still molten and components are well mixed, but then why shouldn't $P$ and $D_{ref}$ be also homogeneously mixed and uniformly distributed.
Additional question: In the figure below, taken from here, I get that the linear function is the isochron, but what is the logarithmic function and how does it help in the dating process/what is its contribution? Thanks