# Logarithms 5

Taught by YourMathGal
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Lesson Summary:

In this lesson on logarithms, we learn about the product property of logarithms and how to write expressions involving logs as a single log using the product property. We derive and prove the property and apply it to various examples, including how to rewrite a sum of logs as a single log and how to rewrite a product as a sum of logs. We also caution against the common mistake of trying to separate out a log of a subtraction or sum problem. Ultimately, this lesson provides a solid foundation for understanding the properties of logarithms and how to manipulate them.

Lesson Description:

In this video, we derive and prove the product property of logarithms and write expressions involving logs as a singe log using the product property.

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

• What is the product property of logs?
• How do you write a logarithmic expression as a sum of logs?
• How do you write the sum of logs as a single log using the product property?
• How do you write log base 2 of 21 as the sum of logs?
• How do you write log base 3 of 11 + log base 3 of 8 as a single log?
• How do you write log base 4 of 5 + log base 4 of 12 as a single log?
• How do you write log base 3 of 2 + log base 3 of x + log base 3 of y^2 as a single log?
• How do you write log base 3 of (x + 2) + log base 3 of (x - 2) as a single log?
• How do you write log base 3 of 5m as a sum of logs?
• How do you write log base 2 of 7xy as a sum of logs?
• How do you derive and prove the product property of logarithms?
• Why does the log base b of xy = log base b of x + log base b of y?
• How do you simplify the log of 4 base 2 + log of 8 base 2?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson explains the often-confusing product property of logarithms that allows you to take a single logarithm and split it up as the sum of logs. It also allows you to combine logarithms that are added with the same base into a single logarithm. This technique can be very useful, but often it is confusing to students. This is a must-see if you are learning about logarithms. Additionally, if you have ever been interested in the proof of why the product property of logs works, the explanation of this proof is excellent in this lesson.