How do you solve e^x - 3e^-x = 2?

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Rod · Answer 1 · 2022-03-30T10:19:57+0000

e^x-3e^-x=2, multiply through by e^x:

e^2x-3=2e^x, arrange as a quadratic:

(e^x)²-2e^x-3=(e^x-3)(e^x+1)=0.

e^x cannot be negative so the solution is e^x=3, making x=ln(3)=1.0986 approx.

How do you solve e^x - 3e^-x = 2?

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