I have a data set that follows the behavior of a function f that depends on a lot of different variables. Let's call two of those variables $a$ and $b$. The specific behavior I'm interested in is $f(a)$ with the influence of b factored out. So I plotted out $f(b)$ and found that it varies depending on another variable, $c$. Fortunately I only care about a handful of discrete c values, so solving for $f(b$) at each of these c values is satisfactory. I found that at a certain $c$, $f(b) = \ln(Ab^3+Bb^2+Cb+D)$ (where I have the specific coefficient values available to me).
I'm not certain how to proceed from here. My intuition tells that simply diving $ \ln (Ab^3+Bb^2+Cb+D)$ out of $f(a)$ at a specific c has the possibility of doing more than just factoring out the b influence. Any help would be appreciated