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About mathematical modeling: I got a curve close to log. How to write the logarithmic equation of this line?
Let y=a+blogx and substitute your data (x 1, y 1), (x2, y2), ..., (xn, yn).

Y 1=a+blogX 1

Y2=a+blogX2

...

Yn=a+blogXn

This is an overdetermined equation with two unknown elements A and B (the number of equations is much larger than the number of unknown elements), which can be solved by least square method, even if

(Y 1-a-blogX 1)^2+...+(Yn-a-blogXn)^2=min

Minimum value, determine a and b, and finally solve an ordinary equation.