Logarithmic Functions Unit Plan

Introduction to Logarithmic Functions

General Outcome:  Develop algebraic and graphical reasoning through the study of relations.

Characteristics of Logarithmic Functions with Base 10 and Base e

Achievement Indicators:

4.1 Express a logarithmic equation as an exponential equation and vice versa.

6.1 Describe, orally and in written form, the characteristics of a logarithmic function by analyzing its graph.
6.2 Describe, orally and in written form, the characteristics of a logarithmic function by analyzing its equation.
6.3 Match equations in a given set to their corresponding graphs.

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Lesson Links: 

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Characteristics of Logarithmic Functions with Base 10 and Base e -- (Youtube)

Discovery Based Learning

1.  Algebra 2: What is Log?  -- TInspire Activity

This lesson involves the one-to-one function f(x)=b^x. In acknowledging the existence of its inverse, students will:

• Use the domain and range of f(x) to determine the domain and range of f^-1(x).
• Interpret the graph of f^-1(x) as the reflection of f(x) across the line y = x.
• Use this inverse relationship to write an equation for the graph of the inverse.
• Recognize the logarithmic notation needed to define the inverse function.
• Use the inputs and outputs of two inverse functions to complete a table. As a result, students will:
• Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.

2.  Graph Logarithms  -- TInspire Activity

Students will investigate the graphs of the family of logarithm functions f(x)=log_a(x), by changing the a-value over the interval 0 less than or equal to a less than or equal to 4. As a result, students will:

• Infer why the conditions a>0 and a≠1 are necessary.
• Determine how the value of a affects the increasing or decreasing behavior of the function.
• Determine the x-intercept, domain, range, and asymptotes.
• Describe the end behavior. NOTE: The time varies for this activity depending on whether students create the TI-Nspire document or use the pre-constructed .tns file.

Assessment For Learning

Evaluating Logarithmic Expressions

Achievement Indicators:

4.1 Express a logarithmic equation as an exponential equation and vice versa.
4.2 Determine the value of a logarithmic expression, such as log ₂ 8, without technology.
4.5 Determine the approximate value of a logarithmic expression, such as log ₂ 9, with technology.

5.4 Solve problems that involve logarithmic scales, such as the Richter scale and the pH scale.

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Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Discovery Based Learning

Assessment For Learning

Laws of Logarithms

Achievement Indicators:

4.3 Develop the laws of logarithms, using numeric examples and the exponent laws.
4.4 Determine an equivalent expression for a logarithmic expression by applying the laws of logarithms.

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Lesson Links

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.

• Click here for a pdf version of the same ERLC Lesson Link.

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Discovery Based Learning

1. Algebra 2: Properties of Logarithms (Nspired Learning Math Classroom)

This lesson is based on observing counter-examples to logarithmic rules and involves comparing the values of several base 2 logarithmic expressions to discover which produce the same result. As a result, students will:

• Generalize these rules for base a, where a is a real number, a > 0 and a ≠ 1.
• Compare these logarithmic properties to their exponential counterparts.

2.  Investigating Laws of Logarithms Powerpoint

3.  James Tanton -- Assessment Thoughts

I think this could be used either as a prompt for Discovery or a Assessment for Learning Piece.

Assessment For Learning

Solving Exponential Equations Using Logarithm

Achievement Indicators:

4.5 Determine the approximate value of a logarithmic expression, such as log ₂ 9, with technology.

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .
5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.

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Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Discovery Based Learning

Assessment For Learning

Modelling Data Using Logarithmic Functions

Achievement Indicators:

6.4 Graph data, and determine the logarithmic function that best approximates the data.
6.5 Interpret the graph of a logarithmic function that models a situation, and explain the reasoning.
6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of logarithmic functions, and explain the reasoning.

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Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Modelling Data using Logarithmic Functions -- (Youtube)

Click here

Discovery Based Learning

Assessment For Learning

Student Exemplars

Please feel free to share any student's work by emailing me at cketsa@gsacrd.ab.ca

Summative Assessments

Click here to assess the summative assessment area. You will need an enrolment key to access this portion of the site.  Please email cketsa@gsacrd.ab.ca for access.

Below is a list of what is available for the Unit.

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Assignments

1.  Unit Assignment with Answer Key -- Ketsa

2.  Assignment 3: Logs -- Williamson

3.  Exponential and Logarithmic Equations Assignment with Answer Key -- McAdam

Quizzes

1.  Chapter 7 Logs Quiz with Answer Key -- Williamson

2.  Quizzy 1 - Functions and Evaluating -- Andersen

Exams

1.  Exponential and Logarithmic Functions Combined Exam with a Blueprint Answer Key -- Ketsa

2.  Summative Test 2 - Logarithmic and Exponential  -- Andersen