## mathivh one year ago Is this a general rule (-ln...)

1. mathivh

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.

2. Loser66

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)

3. Loser66

Not sure about the particular case.

4. Loser66

ok, let apply |dw:1439242653354:dw|

5. Loser66

ok, same.

6. mathivh

Yeah I knew about the particular case, not sure it was correct for every $a,b \in \mathbb{R}$. And apparently it does ;-), thanks again. It seems like I'm becoming one of your regular customers!

7. Loser66