SOLUTION: solve for x lnx + ln(x+7)=2

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Question 637682: solve for x
lnx + ln(x+7)=2
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
solve for x
lnx + ln(x+7)=2
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Adding logs --> multiplying
ln(x*(x+7)) = 2


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=19.4437756042774 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -1.29524516077879, -5.70475483922121. Here's your graph:

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x = (-7/2) ± sqrt(49 + 4e^2)/2
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e and e^2 are just constants.
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