How to solve $\left\lfloor y_1 2^z\right\rfloor -\left\lfloor y_2 2^z\right\rfloor =x$ for $z$ in terms of $y_1,y_2$ and $x$?

Question

Question: Solve $\left\lfloor y_1 2^z\right\rfloor -\left\lfloor y_2 2^z\right\rfloor =x$ for $z$ in terms of $y_1,y_2$ and $x$.

Without the floors it's pretty simple algebra but I don't know what operations I can perform on the floors.