This capacitance follows an inverse log law such that there is an asymptote and discontinuity in the variable value for capacitance

If you wanted to get rid of this asymptote and linearize the capacitance variation how would you go about it?

My idea is to turn the capacitance into a voltage and then linearize that then turn the result back into a capacitance

The issue is of course the conversion but also the mathematics, what function would you apply to an inverse logarithm 1/ln(x) to make it linear and how would you do this with circuits

I don't want the answer but perhaps a push in the right direction, what area of circuit theory should i be looking at

Analog circuits only btw!