$$y = \ln (|\ln x|)$$
Attempt at solution:
For the function to be defined, $|\ln x|> 0$
$\implies ln x > 0 $
$\implies x > 1$ [$\because$ anti-logging both sides.]
But clearly, the function is valid if $x\in(0,1)$ as well. I am not sure what I am doing wrong. I might be doing something completely illegal here. So sorry about that!
I am looking for a mechanical way of solving these types of problems. So solutions which don't involve graphs (if possible) are requested.
Thanks in advance!
Ps. I have no clue on how to begin calculating for the range.