Part 1: Develop your mathematical understanding of logarithms by following the steps below.
Create a free account with khanacademy.org so that you can track and save your progress and achievements. Click on "login" in the top right corner.
A. Learn what logarithms are and how they are related to exponential functions.
Watch the video "Introduction to Logarithms" at
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithms
Afterwards, click the green “Practice this Concept” tab and complete the practice. Save a screenshot
of your progress summary.
B. Learn properties of logarithms
Watch the video "Introduction to Logarithm Properties" at
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithm-properties
Afterwards, click the green “Practice this Concept” tab. Continue practice until you have achieved
mastery. Take a screenshot of your progress summary.
Watch a video of more advanced properties:
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithm-properties--part-2
Afterwards, click the green “Practice this Concept” tab. You may stop once you receive a
message that you are proficient with this topic. Save a screenshot of your progress summary.
C. Learn how to solve logarithmic equations.
Watch the video "The Reason for Logarithms" at
http://www.britannica.com/EBchecked/topic/346146/logarithm
Watch the video "Logarithmic Equations" at
http://www.khanacademy.org/math/algebra/logarithms/v/logarithmic-equations
Take notes on examples from the video. Then create and solve 2 equations. Check your solutions.
Watch the video "Solving Logarithmic Equations" at
http://www.khanacademy.org/math/algebra/logarithms/v/solving-logarithmic-equations
Take notes on examples from the video. Then create your own example in the same format. Solve it
and check your solution.
D. Explore graphs of logarithmic functions.
Explore graphs of logarithmic functions at http://www.analyzemath.com/logfunction/logfunction.html
Save a screenshot of the initial graph and write its equation. Describe domain, range, intercepts, and
asymptotes.
Change 1 parameter at a time, each time saving a screenshot and writing the corresponding equation.
For each new graph, describe domain, range, intercepts, and asymptotes.
Write a summary describing the effect of changing each parameter.
Explore how graphs of exponential functions are related to graphs of logarithmic functions at
http://www.analyzemath.com/inversefunction/inversefunction.html
Select the exponential function in the dropdown box at the top. Describe what you notice about the
graph of the reflection of the exponential function over the line y=x.
Compile all of your artifacts from part 1 and submit to your teacher for review prior to proceeding to part 2.
Part 2: Explore real phenomena related to logarithms as part of the role you have assumed.
You and a partner must choose a role from the task tab and have your choice approved by your
teacher. You may create a role not on the list with prior approval from the teacher.
Next you must research your topic and develop a proposal to address the problem at hand. Use the
resources below to help you understand applications of logarithms and how they are relevant to
your situation. You should not limit yourself to the resources below.
Your final product should be a presentation in electronic or poster form that defines your role, clearly
explains the mathematical connection, and provides justification for the proposal. See the evaluation tab
for more guidance on your final product.
Create a free account with khanacademy.org so that you can track and save your progress and achievements. Click on "login" in the top right corner.
A. Learn what logarithms are and how they are related to exponential functions.
Watch the video "Introduction to Logarithms" at
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithms
Afterwards, click the green “Practice this Concept” tab and complete the practice. Save a screenshot
of your progress summary.
B. Learn properties of logarithms
Watch the video "Introduction to Logarithm Properties" at
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithm-properties
Afterwards, click the green “Practice this Concept” tab. Continue practice until you have achieved
mastery. Take a screenshot of your progress summary.
Watch a video of more advanced properties:
http://www.khanacademy.org/math/algebra/logarithms/v/introduction-to-logarithm-properties--part-2
Afterwards, click the green “Practice this Concept” tab. You may stop once you receive a
message that you are proficient with this topic. Save a screenshot of your progress summary.
C. Learn how to solve logarithmic equations.
Watch the video "The Reason for Logarithms" at
http://www.britannica.com/EBchecked/topic/346146/logarithm
Watch the video "Logarithmic Equations" at
http://www.khanacademy.org/math/algebra/logarithms/v/logarithmic-equations
Take notes on examples from the video. Then create and solve 2 equations. Check your solutions.
Watch the video "Solving Logarithmic Equations" at
http://www.khanacademy.org/math/algebra/logarithms/v/solving-logarithmic-equations
Take notes on examples from the video. Then create your own example in the same format. Solve it
and check your solution.
D. Explore graphs of logarithmic functions.
Explore graphs of logarithmic functions at http://www.analyzemath.com/logfunction/logfunction.html
Save a screenshot of the initial graph and write its equation. Describe domain, range, intercepts, and
asymptotes.
Change 1 parameter at a time, each time saving a screenshot and writing the corresponding equation.
For each new graph, describe domain, range, intercepts, and asymptotes.
Write a summary describing the effect of changing each parameter.
Explore how graphs of exponential functions are related to graphs of logarithmic functions at
http://www.analyzemath.com/inversefunction/inversefunction.html
Select the exponential function in the dropdown box at the top. Describe what you notice about the
graph of the reflection of the exponential function over the line y=x.
Compile all of your artifacts from part 1 and submit to your teacher for review prior to proceeding to part 2.
Part 2: Explore real phenomena related to logarithms as part of the role you have assumed.
You and a partner must choose a role from the task tab and have your choice approved by your
teacher. You may create a role not on the list with prior approval from the teacher.
Next you must research your topic and develop a proposal to address the problem at hand. Use the
resources below to help you understand applications of logarithms and how they are relevant to
your situation. You should not limit yourself to the resources below.
Your final product should be a presentation in electronic or poster form that defines your role, clearly
explains the mathematical connection, and provides justification for the proposal. See the evaluation tab
for more guidance on your final product.