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I have found a multiplicative modulus function, an analogue of absolute value for multiplication. Not a groundbreaking one, i'm sure someone has thought about this before. More specifically it is a function that satisfies:

[tex]\operatorname{MM}(1) = 1[/tex]

[tex]\operatorname{MM}(x^{-1}) = \operatorname{MM}(x)[/tex]

[tex]| \log{x} | = \log{(\operatorname{MM}(x))} \, \forall x \in \mathbb{R}^+[/tex]

[tex]\operatorname{MM}(x) = x \, \forall x \ge 1 [/tex]

[tex]\operatorname{MM}^{-1} (x) = x^{\pm 1}[/tex]

Why isn't this function widely used in mathematics? is it because it can be replaced with [tex]e^{|\ln{x}|}[/tex] ?

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# Multiplicative modulus

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