# Logarithms 6 - Quotient Property of Logs

Taught by YourMathGal
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Lesson Summary:

In this math lesson, we learn about the quotient property of logarithms by deriving it and working through examples. The quotient property states that the logarithm of a quotient is equal to the difference of the logarithm of the numerator and the logarithm of the denominator. We practice applying this property to various problems, including simplifying expressions and writing differences as single logarithms. By the end of the lesson, we have a thorough understanding of how to use the quotient property to solve logarithmic equations.

Lesson Description:

Develops the Quotient property of logs, and provides examples and problems. .

More free YouTube videos by Julie Harland are organized at http://yourmathgal.com

• What is the quotient property of logarithms?
• How do you write log base 3 of x/7 as a difference of logs?
• How do you write log base 2 of 10/11 as a difference of logs?
• How do you write log base x of 2/7 as a difference of logs?
• How do you write log base 2 of 5 - log base 2 of (x + 1) as a single log?
• How do you write log base 5 of x^2 - log base 5 of (x^2 - 1) as a single log?
• How do you write log base 2 of 8/x as a difference of logs and simplify?
• How do you write log base m of m^5/2 as a difference of logs and simplify?
• How do you simplify log base 2 of (32/8) using the quotient rule of logs?
• How do you derive the quotient property of logarithms?
• Why does the quotient property of logarithms work?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson explains and derives the quotient property of logarithms and then does several example problems showing how to go from a single logarithm quotient to a difference of logarithms and also from a difference back to a single logarithm. The results are simplified where possible. All steps in this process are explained. Watching this video will not only show you how and why this property works, but it also gives you practical examples of problems using the rule.