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I ran into the following question:

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what happens when you apply logarithm transformation to a data?

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One thing that is often done is that each value $y_i$ of the variable on the vertical axis is replaced not with $\log y_i$, but with $\mathrm{GM}(y)\cdot\log y_i$, where GM is the geometric mean $(y_1\cdots y_n)^{1/n}$. That way the transformed and untransformed data are both measured in the same units, so that you can make sense of such statements as that one of them had a smaller sum of squares of residuals and is therefore a better fit. – Michael Hardy Oct 27 '12 at 21:04
$y=cx^n\implies \ln y=n\ln x + \ln c$. So any power law becomes a linear equation in logarithms, so the best possible values of $c$ and $n$ can be solved for by least squares methods or other similar things, which is normally much easier than estimating values directly from the original data. – Robert Mastragostino Oct 27 '12 at 23:12

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