Name for property?

Question

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:

$-\log(a/b)=log(b/a)$

$-(\log(a)-\log(b))=\log(b/a)$

$-\log(a)+\log(b)=\log(b/a)$

$\log(b)-\log(a)=\log(b/a)$

$\log(b/a)=\log(b/a)$

Answer 1

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