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

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Question 202848: Write as a single Logarithm: [ln(2) + ln(3) + ln(5)]- ln(7)
Answer by jsmallt9(3758) 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