SOLUTION: I need a little help here: ln(x+9)-ln(x-5)=ln(x+7)-ln(x-4). Apparently there is no solution? Why not x=1/3?!

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Question 468208: I need a little help here:
ln(x+9)-ln(x-5)=ln(x+7)-ln(x-4).
Apparently there is no solution? Why not x=1/3?!
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
ln(x+9)-ln(x-5)=ln(x+7)-ln(x-4).
Apparently there is no solution? Why not x=1/3?!
------------------
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-5%29+=+%28x%2B7%29%2F%28x-4%29
x%2B9%29%2A%28x-4%29+=+%28x-5%29%2A%28x%2B7%29
x%5E2+%2B+5x+-+36+=+x%5E2+%2B+2x+-+35
3x = 1
x = 1/3
----------------
x = 1/3 makes ln(x-5) and ln(x-4) the logs of negative numbers.
--> no solution.

Answer by stanbon(75887) 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[(x+9)/(x-5)] = ln[(x+7)/(x-4)]
----
(x+9)/(x-5) = (x+7)/(x-4)
---
Cross-multiply
x^2 + 5x - 36 = x^2 + 2x - 35
----
3x = 1
x = 1/3
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Why is that not a solution?
If you substitute that into the original equation
you would get:
ln((1/3)+9) - ln((1/3)-5) = ln((1/3)+7 - ln((1/3)-4)]
---
The ln((1/3)-5) and the ln((1/3)-4) are both undefined.
because there is not ln of a negative number.
------
Therefore, no solution.
===========================
cheers,
stan H.