Teaching Schedule for Chapter 5 – Logarithmic Functions NF
Week Date
Time
Ratio
Section
5.1 Common Logarithms
A Definition of Common
Logarithms
B Properties of Common
Logarithms
• Understand the definition of
common logarithms.
• Learn the properties of common
logarithms.
• Apply the properties of common
logarithms to solve problems.
5.2 Logarithmic Equations
• Learn how to solve logarithmic
equations.
• Learn how to solve exponential
equations by converting them into
logarithmic equations.
5.3 Applications of Logarithms
A Sound Intensity Level
B Richter Scale
C Logarithmic Transformation
3
• Teachers should introduce the
definition of common logarithms.
• Teachers may use Activity 5.1 to let
students explore the properties of
common logarithms.
• Teachers may derive the properties of
common logarithms from the laws of
indices.
• Teachers should illustrate the
applications of the properties of
common logarithms with examples.
• Teachers should introduce the concept
of logarithmic equations.
• Demonstrate how to apply the
properties of common logarithms to
solve exponential and logarithmic
equations with examples.
Example
Activity
IT Teaching
Classwork
Further
Practice
Exercise
Animation / Video: p. 5.4, 5.7
Applications of
Logarithms
5-Minute Lecture:
Common
Logarithms
Extra IT Activity:
Properties of
common logarithms
p. 5.6, 5.10 Exercise 5A (p. 5.10)
Level 1: 1 – 23
Level 2: 24 – 40
Rev. Ex. 5 (p. 5.46)
Level 1: 1, 5, 8,
10 – 11
Level 2: 32 – 33,
35 – 36, 38, 40
5.6 – 5.8
Teaching Examples
5.6 – 5.8
Teaching Examples
(Extra) 5.6, 5.7
5-Minute Lecture:
Logarithmic
Equations
p. 5.14
• Appreciate the applications of
• Teachers should use various real-life
logarithms in real-life situations
situations to illustrate the applications of
such as measuring sound intensity
logarithms.
and the magnitude of an earthquake,
and logarithmic transformation.
5.9 – 5.12
Teaching Examples
5.9 – 5.12
Teaching Example
(Extra) 5.10
5-Minute Lecture:
Applications of
Logarithms
5.4 Logarithms to an Arbitrary Base
A Definition of Logarithms to an
Arbitrary Base
B Properties of Logarithms to an
Arbitrary Base
• Understand the definition of
logarithms to an arbitrary base.
• Learn the properties of logarithms
to an arbitrary base.
• Apply the properties of logarithms
to an arbitrary base to solve
problems.
5.13 – 5.15
Teaching Examples
5.13 – 5.15
Teaching Example
(Extra) 5.14
5-Minute Lecture: p. 5.23, 5.25 p. 5.27
Logarithms to an
Arbitrary Base
5.5 Graphs of Logarithmic
Functions and their Properties
A The Graphs of y = logax where
a>1
B The Graphs of y = logax where
0<a<1
C Relationship between Graphs of
Exponential and Logarithmic
Functions
• Understand the logarithmic
functions and their properties.
• Recognize the features of the
graphs of logarithmic functions.
• Understand the relationship
between y = logax and y = ax.
5.16
Activity 5.2
Teaching Example (p. 5.30)
5.16
5-Minute Lecture: p. 5.37
Graphs of
Logarithmic
Functions and their
Properties
IT Activity 5.1:
Properties of graphs
of y = logax for
a>1
Extra IT Activity:
Relationship
between the graphs
of y = ax and
y = logax
2
2
Teaching Guide
5.1 – 5.5
Activity 5.1
Teaching Examples (p. 5.6)
5.1 – 5.5
Teaching Examples
(Extra) 5.3, 5.5
4
2
Teaching Objective
• Teachers should emphasize that
common logarithm is not the only type
of logarithms. Its definition and
properties can be extended to an
arbitrary base a, where a > 0 and a≠1.
• Teachers should introduce the
base-change formula of logarithms.
• Demonstrate how to apply the
properties of logarithms to solve related
problems.
• Teachers may use Activity 5.2 or IT
Activity 5.1 to let students explore the
properties of the graphs of logarithmic
functions.
• Teachers should use the tabular and
graphical representation of exponential
functions and logarithmic functions to
discuss their relationship.
• The concept of inverse function can be
introduced, but its notation and formal
definition are not required.
• Teachers may use Extra IT Activity to
demonstrate the relationship between the
graphs of y = ax and y = logax.
Exercise 5B (p. 5.15)
Level 1: 1 – 14
Level 2: 15 – 30
Rev. Ex. 5 (p. 5.46)
Level 1: 14 – 17, 19,
21, 23 – 24
Level 2: 41 – 42,
46 – 47, 50 – 51
Exercise 5C (p. 5.21)
Level 1: 1 – 7
Level 2: 8 – 12
Rev. Ex. 5 (p. 5.46)
Level 1: 25 – 27
Level 2: 52 – 53
Exercise 5D (p. 5.28)
Level 1: 1 – 25
Level 2: 26 – 43
Rev. Ex. 5 (p. 5.46)
Level 1: 2 – 4, 6 – 7,
9, 12 – 13, 18, 20, 22,
28
Level 2: 29 – 31, 34,
37, 39, 43 – 45,
48 – 49
Exercise 5E (p. 5.37)
Level 1: 1 – 5
Level 2: 6 – 10
Rev. Ex. 5 (p. 5.46)
Level 2: 54 – 55
1
5.6 Historical Development of the
Concept of Logarithms
A The Logarithm Tables
B The Anti-logarithm Tables
C The Slide Rule
• Appreciate the development of the • Teachers can introduce the logarithm
concept of logarithms.
tables, the anti-logarithm tables and the
slide rule.
Basic Topical Worksheets
Key Stage 3 (S1 to S3):
Key Stage 4 (S4 to S6):
40 Percentages (III) 41 Percentages (IV)
80 Common Logarithms NF 81 Logarithms to an Arbitrary Base NF
p. 5.41, 5.42