Simplifying ln(exp(-a) + exp(a)) - Need Help with Homework

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SUMMARY

The discussion focuses on simplifying the expression ln(exp(-a) + exp(a)). Participants clarify that there is no logarithmic rule allowing the simplification of ln(x+y) into ln(x) + ln(y). Instead, they reference the hyperbolic cosine function, cosh(a), which is defined as 1/2(exp(a) + exp(-a)). This insight provides a pathway to simplify the original expression using hyperbolic identities.

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Homework Statement


Hey, does anyone know how to further simplify this:



Homework Equations


ln(exp(-a) + exp(a))?


The Attempt at a Solution

 
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There is no such rule as ln(x+y)=lx+lny if that is what you wanted to know. The most I can think of is that cosh(x)= 1/2(ex+e-x)
 


Thank you, this is good. I was after a trig simplification.
I knew one for 2cos(x) = exp(-ix) + exp(ix) but couldn't remember one without the imaginary.
Ta!
 

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