Question

What is the domain of `arcsin(Ln(x))`?

Answer 1

Let `y=arcsin(lnx)` hence `siny=lnx`

But the domain of `lnx` is `x>0`

The domain of siny is `-1<=siny<=1` hence

`-1<=lnx<=1` hence `e^-1<=x<=e^1`

Finally the domain of `y=arcsin(lnx)` is `D_y=[1/e,e]`