I am trying manipulate an equation with logs, and I am 99% sure that there is something going wrong in my thinking.
I started of with seomthing like this:
$-\log Ae^x$
using log rule $\log AB = \log A + \log B$
(1) $-(\log A + \log e^x)=$
(2)$-\log A - \log e^x=$
(3)$-\log A + \log e^{-x}=$
(4)$-\log A e^{-x}$
which is clearly wrong, I can see that to, but I cannot see where my algebra is failing me, where am I missing the necessary brackets?
The right answer is $(1)$.
Also, $(3)$ is valid.
I think your rule is wrong.
It should be $$\log{AB}=\log|A|+\log|B|,$$ otherwise $$\log4=\log((-2)(-2))=\log(-2)+\log(-2),$$ which is delirium.