Solve the given trigonometry problem

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SUMMARY

The discussion centers on solving the trigonometric equation \(5e^{2x} - 2 - 9e^x = 0\). Participants clarify that pre-multiplying each term by \(e^x\) is incorrect for this specific equation, as it alters the equality and complicates the solution process. Instead, the correct approach involves factoring by \(e^{-x}\) to simplify the equation. The final solution for \(x\) is determined to be \(x = \ln 2\), emphasizing the importance of maintaining the integrity of the equation during manipulation.

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chwala
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Homework Statement
##7 \sinh x + 3 \cosh x = 9##
Relevant Equations
hyperbolic trig. equations
My question is on the highlighted part (circled in red);

Why is it wrong to pre-multiply each term by ##e^x##? to realize ,

##5e^{2x} -2-9e^x=0## as opposed to factorising by ##e^{-x} ## ?

The other steps to required solution ##x=\ln 2## is quite clear and straightforward to me.



1716546593601.png
 
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What makes you think you cannot?
 
...because of this next step:

1716547615185.png


I think i get it now...to find the solution for ##x##, we can solve it as i had indicated but for the integration bit; we have to make use of all the transforms...
 
Last edited:
That solves an entirely different question than the one you asked. The one you asked about asked for the solutions of a particular equality. What that thing is is integrating 1 divided by one of the sides of the equality.
 
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