Finding a curve that balances two logarithmic functions

[mikewinifred]

I have two curves 1+m1*log(x) and 4.5+m2*log(x) [please see the attached picture]. I want to fit a third curve (which might of any equation), which should actually 'balance' the first two curves, so that the error is minimum. My problem is I am not able to get a initial reduced slope in the third curve when I try to fit with an eqn (in excel) of form a+b*log(x). I have a feeling like adding a negative exponential or something similar to that with eqn of form a+b*log(x) we might arrive at a curve similar to curve 3 [please see the attached picture]. Any suggestions? Thanks guys.

 

[Mark44]

I have two curves 1+m1*log(x) and 4.5+m2*log(x) [please see the attached picture]. I want to fit a third curve (which might of any equation), which should actually 'balance' the first two curves, so that the error is minimum. My problem is I am not able to get a initial reduced slope in the third curve when I try to fit with an eqn (in excel) of form a+b*log(x). I have a feeling like adding a negative exponential or something similar to that with eqn of form a+b*log(x) we might arrive at a curve similar to curve 3 [please see the attached picture]. Any suggestions? Thanks guys.

What do you mean by "balance" the first two curves? And what error are you talking about?