Quotient Rule of Logarithms - Problem 1

Using the quotient rule of logarithms to rewrite a logarithm as more than one log. This is often times referred to as expanding. What we have here is a logarithm with two components and we’re dividing. Using the quotient rule logarithms what we can do is split this up and do it, use it as subtraction. What we end up with is log base 7 of 49 in the numerator minus log base 7 of 3. We took our division, used the quotient rule, and turned it into subtraction.

Now just using some simple properties of logs that we know, we already know that log base 7 of 49 is 2. 7² is 49 so this becomes 2 minus log base 7 of 3.

Using the quotient rule and what we know about logs we were able to rewrite this, expand this and rewrite it as 2 different logs, actually 1 log and 1 number.