SOLUTION: e^x-e^-x=1 Hint:Multiply both sides by e^x. Please help!

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Question 831629: e^x-e^-x=1 Hint:Multiply both sides by e^x.
Please help!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
e%5Ex-e%5E%28-x%29=1
e%5E%282x%29-1=e%5Ex
e%5E%282x%29-e%5Ex-1=0
Let u=e%5Ex, u%5E2=e%5E%282x%29,
u%5E2-u-1=0
u+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
u+=+%281+%2B-+sqrt%28+1%2B4+%29%29%2F%282%29+
u+=+%281+%2B-+sqrt%285+%29%29%2F%282%29+
Only the positive solution works in this case since e%5Ex%3E0
e%5Ex=%281%2Bsqrt%285%29%29%2F2
highlight_green%28x=ln%281%2Bsqrt%285%29%29%2F2%29
+graph%28+300%2C+300%2C+-2%2C+2%2C+-2%2C+2%2C+e%5Ex-e%5E%28-x%29%29+