SOLUTION: I have been asked to write 2/3ln(x-3)+4lnx-7ln(2x-5) as a single logarithm with a coefficient of one. I have no idea how to do this, and I would greatly appreciate any help.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have been asked to write 2/3ln(x-3)+4lnx-7ln(2x-5) as a single logarithm with a coefficient of one. I have no idea how to do this, and I would greatly appreciate any help.      Log On


   

Question 1104219: I have been asked to write 2/3ln(x-3)+4lnx-7ln(2x-5) as a single logarithm with a coefficient of one. I have no idea how to do this, and I would greatly appreciate any help.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Use three basic rules for logarithms:
(1) ln%28ab%29+=+ln%28a%29%2Bln%28b%29
(2) ln%28a%2Fb%29+=+ln%28a%29-ln%28b%29
(3) ln%28a%5En%29+=+n%2Aln%28a%29

Using (3)...
%282%2F3%29ln%28x-3%29+=+ln%28%28x-3%29%5E%282%2F3%29%29
4ln%28x%29+=+ln%28x%5E4%29
7ln%282x-5%29+=+ln%28%282x-5%29%5E7%29

Then using (1) and (2)...