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WEEK-18-PROPERTIES-OF-LOGARITHMS
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Created on January 3, 2025
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Transcript
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Objectives
Properties of Logarithms
Power and Change of Base
Summary
Special Logarithms
Product and Quotient
Story
Story
Product and Quotient
Example 1: Let's calculate logarithm base 2 of 32.
x and y
are two numbers.
is the base
Here:
Logarithm of product is the sum of logarithms.
The Product Property
Example 2: Let's calculate logarithm base 3 of 9/3.
x and y
are two numbers.
is the base
Here:
Logarithm of quotient is the subtraction of logarithms.
The Quotient Property
Try It By Yourself
Logarithm of Power and Change of Base
is a power.
Example 3: Let's calculate log base 2 of 64, which is 8².
is a number.
is the base
Here:
The logarithm of a power is the exponent times the logarithm of the base.
The Power Property
is another base.
Example 3: Calculate log₃(25).
is a number.
is a base
Here:
It allows us to convert a logarithm to a different base.
Change of Base Formula
Try It By Yourself
Special Logarithms
Graph
Example 4: Let's calculate log base 10 of 100:
Notation
Base 10
Graph
Example 5: Let's calculate natural logarithm of e:
Notation
Base e (Euler Nummber)
Try It By Yourself
Summary
11TH-PROPERTIES-OF-LOGARITHMS-EN © 2025 by CASURID is licensed under CC BY-NC-ND 4.0
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Welcome 6th graders!
All log base 10 are denoted simply as log, without need to write the base.
MA.912.NSO.1 Generate equivalent expressions and perform operations with expressions involving exponents, radicals or logarithms. MA.912.NSO.1.6 Given a numerical logarithmic expression, evaluate and generate equivalent numerical expressions using the properties of logarithms or exponents. MA.912.NSO.1.7 Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents. ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.
All log base e are denoted as ln, or natural logarithm