I suspect that a function $f(x,y)$ is of the form $f(x,y)=a(bx+c)^{dy+e}$. I have access to several values of $f(x,y)$. How do I proceed numerically to find the parameters $\{a,b,c,d,e\}$?
By plotting $\log f$ versus $\log y$ for a fixed $x$, I would get a linear curve and this would give me hope to find $\{d,e\}$. But getting $\{b,c\}$ is beyond me right now.