SOLUTION: ln(x^2+3x-4)-ln(x+14)=3

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Question 1034961: ln(x^2+3x-4)-ln(x+14)=3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x^2+3x-4)-ln(x+14)=3
ln(x^2+3x-4) = ln(x+14) + 3 = ln(x+14) + ln(e^3)
ln(x^2+3x-4) = ln(e^3*(x+14))
x^2+3x-4 = e^3*(x+14) = e^3x + 14e^3
x^2 + (3-e^3)x - (4+14e^3) = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-17.0855369231877x%2B-285.1975+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-17.0855369231877%29%5E2-4%2A1%2A-285.1975=1432.70557195361.

Discriminant d=1432.70557195361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17.0855369231877%2B-sqrt%28+1432.70557195361+%29%29%2F2%5Ca.




Quadratic expression 1x%5E2%2B-17.0855369231877x%2B-285.1975 can be factored:

Again, the answer is: 27.4683171455397, -10.3827802223519. Here's your graph: