This may be a stupid question, it may not. But I was working on some basic logarithm problems and found out that: $-\log(a/b)=\log(b/a)$ Is there a name for this property?

Here's my proof:







Yes. It is a specific case of the power property of logarithms. $\log{a^p} = p\log{a}$. In this case, $\log{\left(\frac{a}{b}\right)^{-1}} = -\log\left(\frac{a}{b}\right)$.

  • $\begingroup$ Wow! That's awesome, I never thought of it like that! $\endgroup$ – user16795 Apr 4 '14 at 0:12

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