EXPONENTIAL EQUATION LOGARITHMIC EQUATION - Chandler Unified School ...

Algebra 2 16.1 (Day One) Properties of Logarithms

16.1 Notes Date: ___________

Properties of Logarithms

Logarithmic expressions can be rewritten using one or more properties of logarithms.

Learning Target A: I can use the properties of logarithms.

Recall that a logarithm is the exponent to which a base must be raised in order to obtain a given number.

EXPONENTIAL EQUATION LOGARITHMIC EQUATION

=

=

> ,

A) Determine each of the following to identify the definition-based properties of logs: If = ___________,

It follows that = ______, so = _______. Also, = _____, so = _________.

B) Just like we have exponent properties for powers of the same __________, we have log properties for logs of the same base! Fill in the table to determine the properties of operations with logs.

Exponent Properties

Logarithm Properties

Product

=

=

Quotient

=

=

Power

() =

=

Example 1. Expand each expression to be written in terms of log m and log n.

A) 25

B)

3 4

1

Algebra 2 C) 42

D)

4 2

16.1 Notes

Fill out the table with the properties of logarithms that you discovered on the first page.

Properties of Logarithms

For any positive numbers a, m, n, b, ( ), and c ( ), the following properties hold: 1. =

Definition-Based Properties

2. 1 = 0

3. = 1

Product Property of Logarithms Quotient Property of Logarithms

=

=

Power Property of Logarithms

=

Example 2. Express each expression as a single logarithm. Evaluate without a calculator, if possible.

A) ln 18 - 2 ln 3 + ln 4

B) ln 25 + 4 ln 5 - ln 125

C) log 6 + log 11

D) 3 250 - 23 10

E)

1 3

58

-

1 2

59

F)

5 2

716

+

2 3

7125

2

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