# How to interpolate on log-log scales? I.e., How do I create an interpolation function which interpolates Log[x] vs Log[y]?

I would like to build and interpolation function that takes in x & y data points and interpolates between them logarithmically in both x and y. I see that this a reply on this post (Interpolate on log scale) provides a nice way of interpolating along the y-axis; i.e., it linearly interpolates {x, log(y)} and then outputs the interpolated {x', y'} (in other words, it gives f(x)) by exponentiating the result rather than giving {x', log(y')}. What I would like to do is interpolate {log(x), log(y)} and then be given an interpolated function {x', y'} as the output rather than {log(x'), y'} (that is, I want f(x) instead of f(log(x)) ). Is this possible within Mathematica?

• Please show the code that you have tried and what you obtained. May 18, 2021 at 21:16

   if = Exp@*Interpolation[Log@data]@*Log

where data is the table you want to interpolate. Then if[x] returns the interpolation result at point x.