Question

Is this a general rule (-ln...)

Answer 1

Is it generally true that
\[\ln(a/b)=-\ln(b/a)\]

I have a case in which this equality is correct, but I don't know for sure if this holds for every a,b element of R.
My case:
\[-\ln \left|\frac{ c-1 }{ c } \right|=\ln \left|\frac{ c }{ c-1 } \right|\].

I don't require a proof, just a simple explanation is fine.

Answer 2

the first one is correct. Since
ln (a/b) = lna -lnb
and ln (b/a) = lnb -lna
hence -ln(b/a) = -lnb + lna = lna -lnb = ln (a/b)

Answer 3

Not sure about the particular case.

Answer 4

ok, let apply