How do I find the equation of a logarithmic spiral (in polar form) passing through a certain amount of points?

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Let's say I have the necessary amount of points that are needed to find an equation of a logarithmic spiral (in polar form) passing through them. How would I use them to find said equation?

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These two plots are of the SAME data:

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and

enter image description here

The top is $(x,y)$ and the bottom is $(\theta,r)$.

Fitting such data is IDENTICAL!!