SOLUTION: I can not figure out the answer to this problem Ln(x)+Ln(x+2)= -3

Algebra ->  Equations -> SOLUTION: I can not figure out the answer to this problem Ln(x)+Ln(x+2)= -3      Log On


   

Question 664304: I can not figure out the answer to this problem Ln(x)+Ln(x+2)= -3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Ln%28x%29%2BLn%28x%2B2%29=+-3
Ln%28x%28x%2B2%29%29=+-3...rewrite as an exponential:
Remember that if log base e of y+=+x, then e%5Ex+=+y.
Ln%28x%5E2%2B2x%29=+-3
x%5E2+%2B+2x=e%5E-3
x%5E2+%2B+2x=1%2Fe%5E3
x%5E2+%2B+2x+%2B+1%2Fe%5E3=0
now use the quadratic formula and eject any answer that makes x come out negative since you can't do log of a negative:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%281%2Fe%5E3%29+%29%29%2F%282%2A1%29+
x+=+%28-2+%2B-+sqrt%28+4-4%2Fe%5E3+%29%29%2F2+

x+=+%28-2+%2B-+sqrt%28+%284e%5E3-4%29%2Fe%5E3+%29%29%2F2+

x+=+%28-2+%2B-+sqrt%28+4%28e%5E3-1%29%2Fe%5E3+%29%29%2F2+

x+=+%28-2+%2B-+2%29sqrt%28+%28e%5E3-1%29%2Fe%5E3+%29%29%2F2+



x+=+-1+%2B-+sqrt%28+%28e%5E3-1%29%2Fe%5E3%29%29+..take a positive root

x+=+-1%2B+sqrt%28+%28e%5E3-1%29%2Fe%5E3%29%29+...or

x+=+sqrt%28+%28e%5E3-1%29%2Fe%5E3%29%29-1+