I think there's a mistake and it should be:

Now, consider:

Let and you'll get a quadratic in . Solve for , substitute again and take natural logs.

Oh, and I felt the need to point this out:

If you have and you take natural logs of both sides, you take the log of the2/x=e^y - e^-y

In(2/x)=In(e^y)-In(e^-y)

In(2/x)=2y

2arccosechx=In(2/x)

this is totally wrong but I do not know how to continue or to handle problem such as this one. Can any one give me a hint and direction about solving this problem?

Best Regards

Junksentireside i.e. and as you know, in general .