How to logarithmic interpolation?
The general fitting formula for pretty much any function is $F(x)=a*x+b$

so if you have a function inside a function it would be $F(G(x))=a*G(c*x+d)+b$ by virtue of substitution.

You made a tiny error. Instead of $y=a+b \log(cx)$ you probably want $y=a+b \log(cx + d)$

try to fit your function again. a multiplier should never equal to zero, because that would imply you don't have a function of $x$.