Properties of Logarithms

Section 3

Objectives

• Work with the properties of logarithms• Write a logarithmic expression as a sum or

difference of logarithms• Write a logarithmic expression as a single

logarithm• Evaluate logarithms whose base is neither 10

nor e• Graph logarithmic function whose base is

neither 10 nor e

loga10

loga a1

aloga M M

loga ar r

Propertiesof

Logarithms

loga (MN) loga M loga N

logaM

N

loga M loga N

loga Mr r loga M

Properties of Logarithms

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If M N, then loga M loga N.

If loga M loga N, then M N.

Properties of Logarithms

If a1, b 1, and M

are positive real numbers, then

loga M logb M

logb a

Change-of-Base Formula

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Page 527 (8-72 every 4th problem)