Easy logaritmic curve fitting

Question

I am trying to model some measures (lux, ohm) that behave as a logarithmic function.

In order to do it, I've tried to model it with MATLAB by projecting the real values using natural logarithms, then use polyfit to get a linear expression. Then, I want to isolate the variable lux.

What I have so far is:

% Original values from spreadsheet
lux = [1, 5, 10, 50, 100]';
ohm = [100, 35, 25, 8, 6]';

% Logaritmic fitting
x_ = log(lux);
y_ = log(ohm);
p = polyfit(x_,y_,1)

x1 = linspace(x_(1), x_(end), 1000);
y1 = polyval(p,x1);
plot(x_,y_,'ob');
hold on;
plot(x1,y1, 'r');
hold on;

% Get expression
% y = -0.6212x + 4.5944
% log(ohm) = -0.6212 * log(lux) + 4.5944

lfun = @(ohm, a, b) ((ohm/exp(b)).^(1/a));
a = p(1);
b = p(2);
t = linspace(1,100,100);

plot(log(t), log(lfun(t, a, b)), '--g');
hold off;
legend({'points','poly','eq'});

Since I got p = -0.6212 4.5944, I assume that the equation is log(ohm) = -0.6212 * log(lux) + 4.5944. Isolating the variable lux results in:

lux = (ohm / exp(4.5944) ).^(-1/0.6212)

However, as can be seen in the green line, it is not working!

What am I doing wrong?

Answer 1

You're doing everything right except for the plotting, in the first plot you defined the x-axis to be log(lux) and the y-axis to be log(ohm), but to adhere to that in the second case you need to flip the arguments:

plot(log(lfun(t, a, b)), log(t), '--g')

t refers to 'ohm' and must therefore be displayed on the y-axis to coincide with the first plot.