I have a logarithmic spiral of the form $$r=ce^{a\theta}-c$$ Subtracting by $c$ modifies the spiral such that $r(0)=0$.
How do I calculate the slope of the tangent line at a point $(r(\theta),\theta)$?
You can calculate the slope of the tangent line to any polar curve at a given point by using differential calculus like this: https://en.wikipedia.org/wiki/Polar_coordinate_system#Differential_calculus, but I was wondering if it could not be done simpler in this case by for example using this property of logarithmic spirals: https://demonstrations.wolfram.com/TangentOnALogarithmicSpiral/