Log Scale

#statistics #interview

Log isolates exponents, $l o g (2^{3}) = 3 l o g 2$
$l o g (x y) = l o g (x) + l o g (y)$
$l o g (\frac{x}{y}) = l o g (x) - l o g (y)$
Log scale is used where there is fold change.
I.e. 8 times greater than 1 is 8
and 8 times less that 1 is 1/8
But on the scale they are not same distance from 1
But if we take log of them
then $l o g (8)$ is 3 times greater from $l o g (1)$
and $l o g (\frac{1}{8})$ is 3 times less from $l o g (1)$
So the scale becomes comparable

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