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

Question 327577: How do you solve: ln(x)+ln(x+12)=9
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(69443) (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

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 : .

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 - .

The solution is , or
Here's your graph:

No real solutions.
Answer by scott8148(6628) (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
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