Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Quotient Rule of Logarithms  Problem 1
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel 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.
Please enter your name.
Are you sure you want to delete this comment?
Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
i love you you are the best, ive spent 3 hours trying to understand probability and this is making sense now finally”
BRIGHTSTORM IS A REVOLUTION !!!”
because of you i ve got a 100/100 in my test thanks”
Concept (1)
Sample Problems (4)
Need help with a problem?
Watch expert teachers solve similar problems.

Quotient Rule of Logarithms
Problem 1 6,175 viewsSimplify:
log_{7}(49⁄3) 
Quotient Rule of Logarithms
Problem 2 5,412 viewsSimplify:
log_{5}x − log_{5}(x + 3) 
Quotient Rule of Logarithms
Problem 3 5,285 viewslog_{b}(x⁄y) = log_{b}x − log_{b}y
Let m = log_{b}x and n = log_{b}y 
Quotient Rule of Logarithms
Problem 4 1,548 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete