SOLUTION: Solve for x: e^2x + 4e^-2x = 4. X= a. (1/2) ln 2 b. (1/3) ln 2 c. (1/3) ln 3 d. (1/2) ln 3 e. ln 2 f. ln 3 g. none of these

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Question 63903: Solve for x: e^2x + 4e^-2x = 4.
X=
a. (1/2) ln 2
b. (1/3) ln 2
c. (1/3) ln 3
d. (1/2) ln 3
e. ln 2
f. ln 3
g. none of these
Found 2 solutions by stanbon, venugopalramana:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
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.

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
Solve for x: e^2x + 4e^-2x = 4.
LET E^2X =Y
THEN
E^(-2X)=1/E^2X=1/Y...HENCE
Y+ 4/Y =4
SINCE Y IS NOT ZERO...E^X CAN NOT BE ZERO FOR ANY FINITE X
Y^2+4=4Y
Y^2-4Y+4=0
(Y-2)^2=0
Y=2
E^X=2
X=LN(2)
E IS THE ANSWER

X=
a. (1/2) ln 2
b. (1/3) ln 2
c. (1/3) ln 3
d. (1/2) ln 3
e. ln 2
f. ln 3
g. none of these