SOLUTION: 2^x-2^(-x)=4

Question 368115: 2^x-2^(-x)=4
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2^x-2^(-x)=4
Multiply by 2^x
2^(2x) - 1 = 4*2^x
Sub y for 2^x
y^2 - 1 = 4y
y^2 - 4y - 1 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=20 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4.23606797749979, -0.23606797749979. Here's your graph:

y = 1 � sqrt(5)
2^x = 1 + sqrt(5) --- Ignore the negative answer
x*log(2) = log(1 + sqrt(5))
x = log(1 + sqrt(5))/log(2)
x =~ 1.69242

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