Simple inequality with natural logarithm

Question

I need to calculate such inequality.

$ \ln\frac{2x}{x-1} \geq 0 $

I'm new to concept of $ \ln$ and clueless how to move on. Any tips?

Answer 1

Hint:

1. You have to specify the domain of validity of this inequation: $\dfrac{2x}{x-1}$ has to be defined and $>0$. This means $$\frac{x}{x-1}\;\text{ defined and }>0\iff x(x-1)>0. $$
2. In this domain of validity, the log is non-negative if and only if $$\frac{2x}{x-1}\ge 1. $$