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Quotient Rule of Logarithms - Problem 1 4,966 views

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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.