Initial Publication Date: August 16, 2024
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Guiding students through Semi-log and Log-log Plots
An instructor's guide to Log Plots

Kyle Fredrick (Pennsylvania Western University - California, PA)
Yongli Gao (The University of Texas at San Antonio)

Jump to: Challenges for students | Topics not included in the module | Resources

What should students get out of this module?

After completing this module, a student should be able to:

Evaluate data for the spread, or range, to determine the appropriateness of Semi-log or Log-log plots;
Develop graphical relationships;
Interpret graphical data to determine optimal fit of mathematical functions;
Analyze mathematical models to explain and predict the behavior of a system.

Why are these math skills challenging to incorporate into courses?

Undergraduate Earth Science students are generally familiar with graphs and answering questions based on graphical data. However, when pressed, they often can't explain why the axes of a graph may not use a conventional numbering (linear) sequence, often starting at zero. In our experience, simply asking students what a log axis or exponential relationship is generates blank stares or confused responses. Semi-log and log-log representations are common throughout geoscience courses and students need explicit, contextual instruction before introducing data that relies on these scales. Remediating their lack of familiarity takes time. Stepping back to show how the spacing of values on log plots and how these plots can help visualize datasets over many orders of magnitude are important starting points. These steps can help students read and create linear, semi-log, and log-log plots, tasks critical to their ability to analyze and synthesize data.

What don't we include in the page?

The focus of the module is heavily weighted toward reading and interpreting graphs. There are additional The Math You Need for Majors modules addressing Exponential relationships, Logarithms, and Orders of Magnitude. Our module defers to those, especially Logarithms, which emphasizes log rules and calculations involving log arithmetic equations. Both authors are hydrogeologists by training, so the problems and examples tend to fall within that area, though we have made a concerted effort to include examples from across the Earth Science disciplinary spectrum.

Instructor resources

Support for teaching this quantitative skill

One or more other resources that can help instructors teach about this topic. SERC collections such as Teaching Quantitative Skills can be a helpful place to look.