SOLUTION: I am needing help answering this logarithm. {{{ln(x)-3}}}{{{"["}}}{{{2*ln(x-6)-ln(x+6)}}}{{{"]"}}} I have got the answer narrowed down to either {{{ln(x(x+6)^2/(x-6)^3)}}} O

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am needing help answering this logarithm. {{{ln(x)-3}}}{{{"["}}}{{{2*ln(x-6)-ln(x+6)}}}{{{"]"}}} I have got the answer narrowed down to either {{{ln(x(x+6)^2/(x-6)^3)}}} O      Log On


   



Question 242473: I am needing help answering this logarithm.
ln%28x%29-3%22%5B%222%2Aln%28x-6%29-ln%28x%2B6%29%22%5D%22
I have got the answer narrowed down to either ln%28x%28x%2B6%29%5E2%2F%28x-6%29%5E3%29 OR
ln%28x%28x-6%29%5E3%2F%28x%2B6%29%5E2%29
Thanks for your help

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I am needing help answering this logarithm.
ln%28x%29-3%22%5B%222%2Aln%28x-6%29-ln%28x%2B6%29%22%5D%22
I have got the answer narrowed down to either ln%28x%28x%2B6%29%5E2%2F%28x-6%29%5E3%29 OR
ln%28x%28x-6%29%5E3%2F%28x%2B6%29%5E2%29
Thanks for your help

I think you forgot to multiply the 3 by the 2 
when removing the brackets.

ln%28x%29-3%22%5B%222%2Aln%28x-6%29-ln%28x%2B6%29%22%5D%22

Distribute the 3 into the brackets to remove them:

ln%28x%29-6%2Aln%28x-6%29%2B3%2Aln%28x%2B6%29 

Use the rule A%2Aln%28B%29+=+ln%28B%5EA%29 to write the 6 and the
3 coefficients as exponents:

ln%28x%29-ln%28x-6%29%5E6%2Bln%28x%2B6%29%5E3

Use the rule ln%28A%29-ln%28B%29+=+ln%28A%2FB%29 to rewrite the
first two terms:

ln%28x%2F%28x-6%29%5E6%29%2Bln%28x%2B6%29%5E3

Use the rule ln%28A%29%2Bln%28B%29+=+%22ln%28AB%29%22 to rewrite those
two terms:

ln%28+%28x%28x%2B6%29%5E3+%29%2F%28%28x-6%29%5E6%29+%29

Edwin