TITLE: How to solve this logarithm inequality with absolute value as its base?
QUESTION [5 upvotes]: How to deal with this ?
$$\log_{|1 - x|} (x+5)>2 $$
the $|1-x|$ is the base of the logarithm.
I tried this below approach but it seems not the complete solution.
\begin{align}
\frac{\log(x+5)}{\log|1-x|} & > 2\\
{\log(x+5)} & > 2{\log|1-x|}\\
{\log(x+5)} & > {\log|1-x|^2}\\
(x+5) & >|1-x|^2\\
(x+5) & >(1-x)^2\\
(x+5) & >1-2x+x^2\\
x^2-3x-4& < 0
\end{align}
$$ -1<x<4 $$
I also checked with wolframalpha.
https://www.wolframalpha.com/input/?i=log+%5Babsolut(1-x),+(x%2B5)%5D%3C2
I appreciate your help.

REPLY [2 votes]: Look at the pictures. You will see there are two cases to the problem. 
Here is a link to : Wolfram Alpha
Hope this helps. If you need help in solving the individual inequalities, comment and I will show this as well.