Representation of a function with the natural logarithm

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Homework Help Overview

The discussion revolves around expressing the inverse hyperbolic secant function arcsech in terms of the natural logarithm. Participants are exploring the mathematical relationships and manipulations involved in this process.

Discussion Character

  • Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster seeks guidance on how to start expressing arcsech using natural logarithms. Some participants discuss the equation for sech and propose manipulating it to isolate x. Questions arise about maintaining the constancy of sech(x) during these manipulations.

Discussion Status

Participants are actively engaging with the problem, offering different approaches to isolate x in terms of sech(x). There is an exploration of how to express the inverse function, but no consensus has been reached on a specific method or solution.

Contextual Notes

Participants are working under the constraints of expressing a specific function in a particular form, and there is an emphasis on understanding the relationships between the variables involved.

Ry122
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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?
 
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<br /> \textrm{sech}\hspace{1mm}x=\frac{2}{e^{x}+e^{-x}}\Rightarrow e^{2x}-\frac{2e^{x}}{\textrm{sech}\hspace{1mm} x}+1=0<br />
Solve for x (keeping sech(x) constant)
 
How do you keep sech(x) constant exactly?
 
I want to find x from knowing sech x right? so let sech x=a
<br /> e^{2x}-\frac{2e^{x}}{a}+1=0<br />
Solving x, you will obtain an expression containing a, that is the inverse function. x=sech^{-1}a
 

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