SOLUTION: e^x-e^-x=1 Hint: multiply e^x on both sides I know this involves natural log but I have no idea what to do. Please help!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: e^x-e^-x=1 Hint: multiply e^x on both sides I know this involves natural log but I have no idea what to do. Please help!      Log On


   

Question 831686: e^x-e^-x=1 Hint: multiply e^x on both sides
I know this involves natural log but I have no idea what to do. Please help!
Answer by hovuquocan1997(83) About Me  (Show Source):
You can put this solution on YOUR website!
you have e^-x = 1/e^x (convert)
So the equation will become
e^x - 1/e^x = 1
multiply e^x like you said
e%5Ex%2Ae%5Ex+-+1+=+e%5Ex
%28e%5Ex%29%5E2+-+e%5Ex+-+1+=+0
Then you can let e^x = a and the equation will become
a%5E2+-+a+-+1+=+0
You can solve this equation using quadratic formula, then you will get two answer
a = %281%2Bsqrt%285%29%29%2F2
and a = %281-sqrt%285%29%29%2F2
Remember you let e^x = a? Now change a into e^x
You have e%5Ex = %281%2Bsqrt%285%29%29%2F2
Then you use natural log on both side, you will have
x = ln%28%281%2Bsqrt%285%29%29%2F2%29 and then use calculator to find it
And then you find another answer with e%5Ex = %281-sqrt%285%29%29%2F2 using the same method
TA-DAH