Solve the given trigonometry problem

[chwala]

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.

 

[Orodruin]

What makes you think you cannot?

 

[chwala]

...because of this next step:

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...

 

[Orodruin]

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.