Unfortunately, I don't understand the logic behind this. I would have thought that a flat tax in terms of utility would solve for the amount of taxes T in log1

Unfortunately, I don't understand the logic behind this. I would have thought that a flat tax in terms of utility would solve for the amount of taxes T in log10(R/P) - log10((R-T)/P) = C for some constant C across the population. That would correspond to taxing everyone an equal amount of utility, assuming a logarithmic model of utility. If the tax itself is proportional to the utility function, that has the effect of taking much less utility from people with greater R. I'm also unclear on how your C works out. The largest company in the world makes less than $1 trillion per year, so even if P is $1, log10(R/P) is bounded above by 12. Given a US budget of several trillion USD, that seems to make C multiple orders of magnitude bigger. Sorry if I'm missing something. That was my original reason for asking for a formula above.