# Use of natural logarithm transformation on weighted index series

I have a value computed as sum of powers, e.g. $x^5+y^8+z^2$.
The exponent represents the weight for variables, $x, y$ and $z$ in the example above.

Applying natural logarithm on $x^5+y^8+z^2$, I get a graph that more accurately describes what I'm looking for.

What I need help with is understanding why that is: why applying the natural logarithm helps. Or should it be done differently?

Thank you.

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Thanks for helping with formatting Stefan. –  Francisc Dec 9 '12 at 16:20
$$\log(x^5+y^8+z^2) = 5 \log(x) + 8 \log(y) + 2 \log(z)$$ –  user51427 Dec 9 '12 at 16:47
Thanks sunflower, I know that. I'm trying to understand why log(x) works. –  Francisc Dec 9 '12 at 16:54
By the way, you can't break the sum like that. –  Francisc Dec 9 '12 at 17:01