SOLUTION: 8^x - 8^-x = 8

Question 877526: 8^x - 8^-x = 8
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
8^x - 8^-x = 8
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Multiply by 8^x
8^2x - 1 = 8^x

sub for 8^x

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=5 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1.61803398874989, -0.618033988749895. Here's your graph:

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Ignore the negative solution
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8^x =~ 1.618
x*log(8) = log(1.618)
x = log(1.618)/log(8)
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