How do I find the X values of "e^x - e^(-x) = 0 " and " - (1/e^x) + e^x = 0"
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How do I find the X values of "e^x - e^(-x) = 0 " and " - (1/e^x) + e^x = 0"

[From: ] [author: ] [Date: 11-05-25] [Hit: ]
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I never found this type of equations before. If someone could tell me how they are solved and hopefully even tell me what's the name of this type of equation so I can check it into google or something.
Cheers, people!

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These are just exponential equations. For the first:

e^x - e^(-x) = 0.........rearrange

e^x = e^(-x)..............take ln of both sides (ln e^x = x)

x = -x...............only solution is x = 0

Second equation: - (1/e^x) + e^x is identical to the first equation; 1/e^x = e^(-x) only the order of the terms is reversed. Same solution.

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Search for 'wolfram alpha' in google and type the equation in there, it generates the X values including working.

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1.)e^x-1/e^x=0
e^2x-1=0
(e^x-1)(e^x+1)=0
e^x=1
e^x=-1
lne1=x
x=0
1
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