Breaking down an average in a nonlinear function into its contributing components

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Originally I was given a moving average that I had to break down to its proportions and display, so business analysts could anticipate the impact of the first element in the average being dropped (i.e. A bar chart being able to see how significant the first element is to the total when making decisions)

$ result = \dfrac{x+y+z}{3}$

$ proportion_x = result \cdot \dfrac{x}{x+y+z} $

Such that $ proportion_x + proportion_y + proportion_z = result $

However, this average is now logarithmically normalized before the final output:

$ result = \left(\log \left(\dfrac{x+y+z}{3}+ 10\right)-1\right)\cdot 10$

Is it still possible to produce this component breakdown for $x, y,$ and $z$ accurately now that the relationship is non-linear?