The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

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WORKSHEET 8.21: USING THE PROPERTIES OF LOGARITHMS

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The properties of logarithms may be used to express a sum, difference, or product of a

logarithm as a single logarithm. Follow the steps below:

1. Identify which of the following properties apply to the problem:
   
   
   • First property:logaMN=logaM+logaN
   
   
   • Second property:logaM
     N
   
   
   
   

=logaM−logaN

• Third property:logaMk=klogaM

2. Apply the third property before using the first or second property.


3. Simplify, if possible.

EXAMPLES

Write each expression as a single logarithm.

Example 1:Only the first property applies.

loga 5 +loga 4 =log 220

Example 2:Apply the third property, then apply the second property.

3loga^4 −loga^2 =loga^43 −loga^2 =loga^64 −loga^2 =loga

64

2

=loga 32

DIRECTIONS: Write the expressions as a single logarithm.

1. loga 10 −loga 2 2. 2loga 3 +loga 4


2. −loga

1

4

1

2

loga 16 +loga 3

CHALLENGE:Terri rewrote

1

2

loga 64 +loga2asloga128. Is she correct?

Explain your answer.

315

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.