Versatile logarithmic potentiometer law model.

log-pot-law.m

% travel is the location of the wiper along the pot from 0 to 1 
travel = linspace(0,1,1000);

% Define the factor of resistance at the middle pot position
mid = 0.15;

% b is the base of the exponential equation
b = (1/mid - 1)^2;

% a is the multiple and also the offset
a = 1/(b-1);

% Calculate the resistance
resistance = a*b.^travel - a;

figure;
plot(travel,resistance)
xlabel('Potentiometer Position'); ylabel('Resistance Factor');