Economists have the natural log problem

They want to integrate quanties as if they are infinitely divisible.  Physics engineering models can do this because the bubbles of the vacuum are so much smaller than any of their approximations.  Quantum physicists learned how to avoid the problem.  But economics is all quant, none of it is infinitely divisible, there is no such thing as 10.56 eggs in a carton, or 4.73 of an automobile.

So their supply and demand function is a poor approximation, while the engineers charge model is quite accurate. Using a poor approximation is OK, if the economist knows what he is doing. I use log, often, but I know in the real world that will be a finite log in some integer base.