SOLUTION: question: ln(x+9)-ln(x+5)=ln(x+7)-ln(x-4) I come up with x=1/3, but my answer key says "no solution". How come? Thanks, Jessica

Algebra ->  Test -> SOLUTION: question: ln(x+9)-ln(x+5)=ln(x+7)-ln(x-4) I come up with x=1/3, but my answer key says "no solution". How come? Thanks, Jessica      Log On


   

Question 467863: question:
ln(x+9)-ln(x+5)=ln(x+7)-ln(x-4)
I come up with x=1/3, but my answer key says "no solution". How come?
Thanks,
Jessica
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x+9)-ln(x+5)=ln(x+7)-ln(x-4)
==> ln%28%28x%2B9%29%2F%28x%2B5%29%29+=+ln%28%28x%2B7%29%2F%28x-4%29%29
==>+%28x%2B9%29%2F%28x%2B5%29+=+%28x%2B7%29%2F%28x-4%29
==> x%5E2+%2B+5x+-+36+=+x%5E2+%2B+12x+%2B+35
==> -71 = 6x
==> x = -71/6
But this x-value will NOT satisfy the original equation because of the terms x+9, x+5, x+7, and x-4 will all give negative values after substitution of x = -71/6, and so there is no solution to the equation.