Question 270973: e x+ e -x=5
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If you mean
e^x + e^-x = 5 then
x = inv hyperbolic cosine (2.5)
x =~ 1.566799 (via calculator)
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The long way
e^x + e^-x = 5
Multiply by e^x
e^2x + 1 = 5e^x
e^2x - 5e^x + 1 = 0
It's a quadratic in e^x
e^x = (1/2)*(5 ± sqrt(21))
e^x =~ 4.7912878, 0.2087
x = log(4.79..., 0.2087)
x = ± 1.566799
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