Logarithmic Functions As Inverses Worksheet
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Algebra II
Notes 8.3
Logarithmic Functions as Inverses
Objective: To write and evaluate logarithmic expressions.
To graph logarithmic functions.
Vocabulary and Key Concepts
Writing and Evaluating Logarithmic Expressions
The magnitude of an earthquake is a measure of the amount of energy released
at its source. The Richter scale is an exponential measure of earthquake
magnitude. An earthquake of magnitude 5 releases about 30 times as much
energy as an earthquake of magnitude 4. (p 438)
0
1
2
3
4
5
6
7
8
9
E∙30
E∙30
2
E∙30
3
E∙30
4
E∙30
5
E∙30
6
E∙30
7
E∙30
8
E∙30
9
E
Compare the amount of energy release in an earthquake that registers 6 on the
Richter scale with one that registers 3.
In 1997, an earthquake in Alabama registered 4.9 on the Richter scale. In 1999,
one in California registered 7.0. Compare the energy released in the two quakes.
The exponents used by the Richter scale as shown in the examples are called
logarithms or logs.
Logarithm
The logarithm to the base b of a positive number y is defined as follows:
x
If y = b
, the log
y = x.
b
The logarithm of a negative number or zero is undefined.
Class Examples:
Write each true equation in logarithmic form.
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EX 1: 25 = 5
EX 2: 729 = 3
EX 3:
2
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