SOLUTION: ln(x-1)-ln(x+1)=ln(x+5)

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Question 143215: ln(x-1)-ln(x+1)=ln(x+5)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

+ln%28x-1%29-ln%28x%2B1%29=ln%28x%2B5%29

Use this principle of logarithms:  ln%28A%29-ln%28B%29=ln%28A%2FB%29

to rewrite the left side;

ln%28%28x-1%29%2F%28x%2B1%29%29=ln%28x%2B5%29

Now use the principle that ln%28A%29=ln%28B%29 can be written as A=B
to rewrite the whole equation:

%28x-1%29%2F%28x%2B1%29=x%2B5

Do you know how to solve that?  If not post again asking how.
You get

x=-3, x = -2

But these must check in the original problem.

+ln%28x-1%29-ln%28x%2B1%29=ln%28x%2B5%29

Substitute x=-3 in the original

+ln%28-3-1%29-ln%28-3%2B1%29=ln%28-3%2B5%29

+ln%28-4%29-ln%28-2%29=ln%282%29

But there can be no logarithm of a negative number
(except in advanced mathematics, but never in ordinary algebra).

So -3 is NOT a solution

Substitute x=-2 in the original

+ln%28-2-1%29-ln%28-2%2B1%29=ln%28-2%2B5%29

+ln%28-3%29-ln%28-1%29=ln%283%29

But, again, there can be no logarithm of a negative number
in ordinary algebra.

Therefore -2 is not a solution either.

Therefore there is no solution to the equation.

Edwin