Representation of a function with the natural logarithm

[Ry122]

I've been asked to express the inverse hyperbolic secant function arcsech in terms of the natural logarithm and am unsure as to where to begin in solving such a problem?
could someone please point me in the right direction?

 

[hunt_mat]

$$\textrm{sech}\hspace{1mm}x=\frac{2}{e^{x}+e^{-x}}\Rightarrow e^{2x}-\frac{2e^{x}}{\textrm{sech}\hspace{1mm} x}+1=0$$
Solve for x (keeping sech(x) constant)

 

[Ry122]

How do you keep sech(x) constant exactly?

 

[hunt_mat]

I want to find x from knowing sech x right? so let sech x=a
$$e^{2x}-\frac{2e^{x}}{a}+1=0$$
Solving x, you will obtain an expression containing a, that is the inverse function. $$x=sech^{-1}a$$