How to invert this function? I need to invert this function:
$$
y=\frac{\ln(x)}{\ln(x-1)}+1
$$
The domain is real (for x>1 and x!=2)
Why can't we just divide it like this:
$$
y=ln(x-(x-1))+1
$$
and then it's:
$$
y=ln(1)+1
$$
so it seems wrong.
Where did I make the mistake?

Yes, this is wrong, because you can use the property of ln, only when $ln \left ( \frac{a}{b} \right )=ln(a) - ln(b)$
Try to use the inverse of ln, we know from lections that it is the exponential function e.
