SOLUTION: How do I change this to a quotient or product? {{{ log(4,(x+3)) + log(4,(x-3)) }}}

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Question 408784: How do I change this to a quotient or product?
+log%284%2C%28x%2B3%29%29++%2B+log%284%2C%28x-3%29%29+
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
+log%284%2C%28x%2B3%29%29++%2B+log%284%2C%28x-3%29%29+
I think you have been asked to rewrite your expression as the log of a product or quotient. If so, there are a couple of properties fo logarithms for this:
  • log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Aq%29%29
  • log%28a%2C+%28p%29%29+-+log%28a%2C+%28q%29%29+=+log%28a%2C+%28p%2Fq%29%29
As you can see, the first property applies if there is a "+" between the two logarithms and the second one applies if there is a "-".

These properties require
  • Two logarithms of the same base.
  • Two logarithms with coefficients of 1.

Your logarithms meet both requirements. Your logarithms have a "+" between them so the first property applies. So: