Question 63903
e^2x + 4e^-2x = 4
Multiply thru by e^(2x) to get:
e^4x + 4 = 4e^2x
Rewrite as:
(e^2x)^2-4(e^2x)+4=0
This is a quadratic with variable e^2x.
Let e^2x=w, then rewrite the equation as:
w^2-4w+4=0
(w-2)^2=0
w=2
Therefore e^2x=2
Take the natural law of both sides to get:
2x=ln2
x=(1/2)ln2
Cheers,
Stan H.