SOLUTION: Write as a single Logarithm: [ln(2) + ln(3) + ln(5)]- ln(7)

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Write as a single Logarithm: [ln(2) + ln(3) + ln(5)]- ln(7)      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 202848: Write as a single Logarithm: [ln(2) + ln(3) + ln(5)]- ln(7)
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
%28ln%282%29+%2B+ln%283%29+%2B+ln%285%29%29+-+ln%287%29
There are a couple of properties of logarithms which can be used to combine logarithms:
  • log%28%28a%29%29+%2B+log%28%28b%29%29+=+log%28%28a%2Ab%29%29
  • log%28%28a%29%29+-+log%28%28b%29%29+=+log%28%28a%2Fb%29%29
These properties apply not just for base 10 logs. They apply as long as the base of all three logs (the two on the left and the one on the right) are the same.

Now let's use the first one to "add" the first three logs:
%28ln%282%2A3%29+%2B+ln%285%29%29+-+ln%287%29
ln%282%2A3%2A5%29+-+ln%287%29
ln%2830%29+-+ln%287%29
Now we can use the second property to "subtract" the remaining logs:
ln%2830%2F7%29