Would You Rather Listen to the Lesson?
|
Change of Base Formula
loga x = ( logb x ) / ( logb a )
Multiplication Rule
The log of a product is the sum of the logs.
loga xy = loga x + loga y
Division Rule
The log of a quotient is the difference of the logs.
loga (x/y) = loga x - loga y
Raising to a Power Rule
loga xr = r * loga x
Summary - Properties of Logarithms
- The log of a product is the sum of the logs
- The sum of the logs is the log of the products
- The log of a quotient is the difference of the logs
- The difference of the logs is the log of the quotient
- The exponent on the argument is the coefficient of the log
- The coefficient of the log is the exponent on the argument
Most Common Mistakes
- The log of a sum is NOT the sum of the logs. The sum of the logs is the log of the product. The log of a sum cannot be simplified.
loga (x + y) ≠ loga x + loga y
- The log of a difference is NOT the difference of the logs. The difference of the logs is the log of the quotient. The log of a difference cannot be simplified.
loga (x - y) ≠ loga x - loga y
- An exponent on the log is NOT the coefficient of the log. Only when the argument is raised to a power can the exponent be turned into the coefficient. When the entire logarithm is raised to a power, then it can not be simplified.
(loga x)r ≠ r * loga x
- The log of a quotient is not the quotient of the logs. The quotient of the logs is from the change of base formula. The log of a quotient is the difference of the logs.
loga (x / y) ≠ ( loga x ) / ( loga y )
Do you have a Sub on Log Day? Here you go...
Here is Your Free Content for This Lesson!
Properties of Logarithms Worksheet, Word Docs & PowerPoints
To gain access to our editable content Join the Algebra 2 Teacher Community!
Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards.
Properties of Logarithms - PDFs
8-4 Assignment - Properties of Logarithms (FREE)
8-4 Bell Work - Properties of Logarithms (FREE)
8-4 Exit Quiz - Properties of Logarithms (FREE)
8-4 Guided Notes Student Edition - Properties of Logarithms (FREE)
8-4 Guided Notes Teacher Edition - Properties of Logarithms (Members Only)
8-4 Lesson Plan - Properties of Logarithms (Members Only)
8-4 Online Activities - Properties of Logarithms (Members Only)
Want access to everything?
Simply click the image below to Get All of Our Lessons!
Don't forget to Pin this lesson!

Head’s? Their head’s what? Shouldn’t there be no apostrophe there? Apols for nitpicking
(Found on https://algebra2coach.com/properties-of-logarithms/)
Good catch, thank you. Fixed. 🙂
The slideshow link does not work, it says page not found.
thanks for letting us know! it’s fixed.