SOLUTION: How do you solve: ln(x)+ln(x+12)=9

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Question 327577: How do you solve: ln(x)+ln(x+12)=9
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x)+ln(x+12)=9
Adding logs --> multiplication
ln(x*(x+12)) = 9
x*(x+12) = e^9
x%5E2+%2B+12x+-+e%5E9+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B8103.08392757538+=+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=%2812%29%5E2-4%2A1%2A8103.08392757538=-32268.3357103015.

The discriminant -32268.3357103015 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -32268.3357103015 is + or - sqrt%28+32268.3357103015%29+=+179.63389354546.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B8103.08392757538+%29

No real solutions.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
adding logs is analogous to multiplying quantities

ln[x(x+12)] = 9

x^2 + 12x = e^9 ___ x^2 + 12x - e^9 = 0

use quadratic formula to find x