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E^x3=e^x someone please help me figure out how to solve the exponential equation! I keep coming up with this being undefined!!!
 one year ago
 one year ago
E^x3=e^x someone please help me figure out how to solve the exponential equation! I keep coming up with this being undefined!!!
 one year ago
 one year ago

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whpalmer4Best ResponseYou've already chosen the best response.1
\[e^{x3} = e^{x}\]Is that the equation? Are you doing exponentials with complex numbers?
 one year ago

jennagBest ResponseYou've already chosen the best response.0
No it is e^x  3 = e^x
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[e^x3=e^{x}\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
are you trying to solve for x?
 one year ago

jennagBest ResponseYou've already chosen the best response.0
Yes! I believe that's what you do when you are solving An exponential equation right?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
\[e^x3=e^{x}\]\[e^x3+e^{x}=0\]\[e^{2x}3e^x+1=0\] now substitute \(e^x=m\) \[m^23m+1=0\] solve this for m
 one year ago

jennagBest ResponseYou've already chosen the best response.0
Would it be sqrt 3m1, and sqrt 3m1
 one year ago

jennagBest ResponseYou've already chosen the best response.0
Sorry I'm on my iPad so I. Not typing it correctly
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
i got \[m=\frac{3\pm\sqrt5}{2}\]
 one year ago

jennagBest ResponseYou've already chosen the best response.0
Woahhh, okay I'm way off! How did you come up with that?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
quadratic formula?
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
to get x , just take the natural logarithm of m
 one year ago

jennagBest ResponseYou've already chosen the best response.0
Got it, was doing it wrong :) thank you!!!!
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
ill check your final result when you get there, if you want
 one year ago

whpalmer4Best ResponseYou've already chosen the best response.1
@jennag just for your edification, there's a thing called the hyperbolic cosine function, \(\cosh x\) which happens to be \[\cosh x =\frac{e^xe^{x}}{2}\]Your problem could have been written as \[2 \cosh x = 3\]Looks so cute and innocent, doesn't it? :)
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.2
note that: \[\cosh x=\frac 32\]\(\qquad\Downarrow\)\[x=\pm\operatorname{arccosh}\frac 32\]
 one year ago
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