How Should Relative Changes be Measured?

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Abstract
Various indicators of relative change (or difference) are considered. It is shown that the log change defined by log e (y/x) is the only symmetric, additive, and normed indicator of relative change. It is proposed that the values of the log change in percent, 100 log e (y/x), be denoted by the symbol L%, the log percentage. It is hoped that the symmetric and additive log percentages will gradually replace the ordinary asymmetric and nonadditive percentages.

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