Section: Module 5: Lesson 3: The Log Scales | Intro to Algebra & Trigonometry | NextGenU.org

  • Student Learning Outcomes:
    Upon completion of this lesson, you will be able to:
    • Explain what a semi-log plot is, and how it is used.
    • Explain the difference between arithmetic and logarithmic line charts.
    Approximate time required for the readings for this lesson (at 144 words/minute): 3 hours and 5 minutes.

    Click here to start this lesson
    • Required Learning Resources and Activities
    • What's a Semi log plot and how can you use it for Covid-19 data? (10 minutes)

      Wired for Science Magazine- 2020

    • Read the entire article. (10 minutes)

      Pennsylvania Department of Health - Tools of the Trade- 2022

    • In this activity, you will solve a case problem about the height and circumference of a given material. Then, you will plot the graph and the log-log values.

      Step 1. Review

      Review this background information before studying the case problem for this activity:

      Background

      Do the physical functions of biological organisms change as the size of the organism changes? For example, does the flight speed of a bird increase as the length of its wings increase? Does the metabolic rate of a mammal increase as the mammal gets larger? Does the height of a California redwood tree increase as the circumference of its trunk increases?

      There are several mathematical equations used to model the relationship between these variables. One possible equation is


      y= mx\( \frac{3}{4} \)


      This type of function (equation) is called a power function.

      Another possible function that models such relationships is the exponential function.

      If the model is a power function, which is not linear, it can be transformed into a logarithm function, which will form into a straight line, as the following shows.

      We take the power function 7455 and take the log of both sides. We will have


      log y= log (axm)= log a + logxm = log a + m log x

      Now, we know that the general form of the equation for a line is Y = mX + a.

      If we let   Y= log y,  A=log a, X= log x

      Then  log y= m log x + log a becomes Y = mX + a, which is a straight line. So, a power function will plot as a straight line on a log-log graph.

      Step 2. Analyze

      Analyze the case problem below.

      8484

      Step 3. Respond

      Respond to the case problem by fulfilling all the required output for this activity. Plot the required data using the systems below:

      Log-log scale paper

      Step 4. Share

      To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).


      Step 5: Interact

      To complete the activity, you will need to reply to at least two posts made by your peers in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

      OPTIONAL Step 6: Interact (10 minutes)

      If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”



    • quiz icon
      Quiz: Module 5: Lessons 2 - 3

      To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

      TO PASS THIS QUIZ YOU MUST OBTAIN A SCORE OF 80%.

      Not available unless: The activity Quiz: Module 5 is marked complete
    • To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

    • Additional Resources for Optional Learning
    • Watch the video. (12 minutes)

      Khan Academy-2022

    • Watch the video. (12 minutes)

      Khan Academy-2022