Dear Math-Helpers.
I'm having a really hard time to find the inverse of the following six-parameter sigmoidal function:
y = c + k*log(x) + (d-c)/(1+exp(b*(log(x)-log(e))))^f
k, c, d, e and f are parameters.
I need to solve the function to x.
Any hints on what transformations are necessary?
If I omit k*log(x) it's easy, but this term makes it hard somehow...
Thanks in advance,
ans
exp(b(log(x)- log(e))= exp(log(x^b))e^{-blog(e)) (I am assuming here that the "e" is just some constant- NOT the base of the exponential function since you have written that as "exp(x)", not "e^x") and exp(log(x^b))= x^b. That equation will have "log(x)" and powers of x. Looks to me like you will need the Lambert W function.