chwala
Gold Member
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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.
![Handwritten working solving 7 sinh x + 3 cosh x = 9 using exponential forms, reducing to 5e^x - 2e^(-x) - 9 = 0, then a boxed step e^(-x)[5e^(2x) - 9e^x - 2] = 0 crossed out with the note: cannot pre-multiply both sides by e^x as a variable.](https://www.physicsforums.com/attachments/1716546593601-png.345859/ "1716546593601.png")
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.