SOLUTION: Solve for x algebraically: ((e^x)-(e^-x))/2=5. Consider exponential equations of quadratic type. I think the answer is supposed to be x=ln(5+sqrt(26)) but I can't figure out the

Question 974322: Solve for x algebraically: ((e^x)-(e^-x))/2=5. Consider exponential equations of quadratic type.
I think the answer is supposed to be x=ln(5+sqrt(26)) but I can't figure out the steps to get it. So far I have (1/2)((e^x)-(e^-x))-5=0. From here I'm lost.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Solve for x algebraically: ((e^x)-(e^-x))/2=5
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Multiply by e^x

Sub u for e^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=104 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 10.0990195135928, -0.0990195135927845. Here's your graph:

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The answer matches.

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