SOLUTION: Solving logarithmic equations the problem is ln x + ln (x+3) = 1 I first combined the ln ln [x(x+3)] = 1 ln x (squared) + 3x = 1 then I don't know what to do.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solving logarithmic equations the problem is ln x + ln (x+3) = 1 I first combined the ln ln [x(x+3)] = 1 ln x (squared) + 3x = 1 then I don't know what to do.       Log On


   

Question 403854: Solving logarithmic equations
the problem is ln x + ln (x+3) = 1
I first combined the ln
ln [x(x+3)] = 1
ln x (squared) + 3x = 1
then I don't know what to do.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
ln x + ln (x+3) = 1
I first combined the ln
ln [x(x+3)] = 1
ln x (squared) + 3x = 1
------------------
ln%28x%5E2+%2B+3x%29+=+1+=+ln%28e%29
x%5E2+%2B+3x+=+e
x%5E2+%2B+3x+-+e+=+0
e is a constant, ~2.71828
Solve the quadratic for x
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-2.71828+=+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=%283%29%5E2-4%2A1%2A-2.71828=19.87312.

Discriminant d=19.87312 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+19.87312+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+19.87312+%29%29%2F2%5C1+=+0.728963884857716
x%5B2%5D+=+%28-%283%29-sqrt%28+19.87312+%29%29%2F2%5C1+=+-3.72896388485772

Quadratic expression 1x%5E2%2B3x%2B-2.71828 can be factored:
1x%5E2%2B3x%2B-2.71828+=+%28x-0.728963884857716%29%2A%28x--3.72896388485772%29
Again, the answer is: 0.728963884857716, -3.72896388485772. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-2.71828+%29