SOLUTION: The following questions are driving me crazy, please help!!!!! 1) Express as a single logarithm with a coefficient of 1. 2 In x -5 In y 2) Writh the logarithm in expanded form.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The following questions are driving me crazy, please help!!!!! 1) Express as a single logarithm with a coefficient of 1. 2 In x -5 In y 2) Writh the logarithm in expanded form.      Log On


   

Question 162960: The following questions are driving me crazy, please help!!!!!
1) Express as a single logarithm with a coefficient of 1. 2 In x -5 In y
2) Writh the logarithm in expanded form. log3(x^2y)3
The question donot come from a text book. My course is online and are questions posted by instructor.
I would be very appreciative if someone could help me solve these problems. I did not began to solve because I donot understand what is being asked.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Your ability to solve these problems relies on your knowing the rules of logarithms!
"Product rule" Log%5Bb%5DM+%2B+Log%5Bb%5DN+=+Log%5Bb%5D%28M%2AN%29
"Quotient rule" Log%5Bb%5DM+-+Log%5Bb%5DN+=+Log%5Bb%5D%28M%2FN%29
"Power rule" p%2ALog%5Bb%5DM+=+Log%5Bb%5DM%5Ep
Now let's apply these to your problems:
1) 2%2Aln%28x%29+-+5%2Aln%28y%29 First apply the "power rule" to get:
ln%28x%5E2%29+-+ln%28y%5E5%29 Now apply the "quotient tule" to get:
highlight%28ln%28x%5E2%2Fy%5E5%29%29
2) Log%5B3%5D%28x%5E2y%29%5E3 Rewrite this by expanding the argument of the logarithm %28x%5E2y%29%5E3+=+%28x%5E6%2Ay%5E3%29
Log%5B3%5D%28x%5E6%2Ay%5E3%29 Now apply the "Product rule" to get:
Log%5B3%5D%28x%5E6%29+%2B+Log%5B3%5D%28y%5E3%29 Now you can apply the "Power rule" to get:
highlight%286%2ALog%5B3%5D%28x%29+%2B+3%2ALog%5B3%5D%28y%29%29