SOLUTION: ln(x)+ln(x-8)=5 I'm supposed to solve for x and I'm lost. I did it the way I thought it should be done but I got it wrong.

Question 704682: ln(x)+ln(x-8)=5
I'm supposed to solve for x and I'm lost. I did it the way I thought it should be done but I got it wrong.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
ln(x)+ln(x-8)=5
ln((x)(x-8)) = 5
(x)(x-8) = e^5
x^2-8 = e^5
x^2-8x = e^5
x^2-8x-e^5 = 0
Solving using the "quadratic formula" yields:
x = {16.82, -8.82}
Since you can't take the ln of a negative number, the -8.82 is an extraneous solution. Throw it out leaving:
x = 16.82
.
Details of quadratic follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=657.652636410308 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 16.8223694808166, -8.8223694808166. Here's your graph:

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