Guiding students through Logarithms
An instructor's guide to Logarithms
Kelly Deuerling (University of Nebraska Omaha)
Alex Manda (East Carolina University)
What should students get out of this module?
After completing this module, a student should be able to:
- Solve Earth science problems using logarithmic expressions
- Use rules and identities of logarithms to re-arrange logarithmic or exponential expressions
- Solve logarithmic expressions with bases other than 10 by converting them to log base 10 expressions
Why are these math skills challenging to incorporate into courses?
Logarithms are often addressed in math classes (algebra, pre-calculus, calculus) where there is limited Earth science context. Therefore, students do not learn to recognize the broad utility of logarithms in the Earth sciences. Students often have some intuitive knowledge of exponential equations and what they mean. However, evaluation of exponential equations may require the use of logarithms to simplify and seeing "log" or "ln" in an equation may lead to students losing interest or focus.
Students may not remember the rules for working with logarithms (e.g., the log of a product is the sum of the logs; the log of a quotient is the difference of the logs etc.). Additionally, students may struggle with using a scientific calculator or spreadsheet to solve logarithmic expressions owing to lack of familiarity with keying in logarithmic expressions and functions.
What we don't include in the page?
Exponential expressions: This module does not go into great detail about how to use exponential expressions, and the rules of exponents. Exponential expressions are covered in a different module: Exponential equations
The module does not explicitly address the process of linearizing exponential and power law equations. Rather, the module focuses on solving exponential and/or power law equations that are already in linear/logarithmic form.
This module does not include processes related to solving logarithmic equations with multiple unknown variables, and it also does not discuss plotting data on log-log and semi-log plots.
Instructor resources
Support for teaching this quantitative skill
- Teaching logarithms (logs) and links therein (Eric Baer)
- A Simple Way to Teach Logarithms (Richard Hammack & David Lyons)
Examples of activities that use this quantitative skill
- Earthquake Magnitude: How Can We Compare the Sizes of Earthquakes? - Compares earthquake intensities and discusses the logarithmic/exponential relationship of the magnitude scale.
- Carbon Sequestration in Campus Trees - Discusses allometric relationships expressed as power functions and how to use logarithms to simplify and visualize the amount of carbon stored in various types/sizes of trees.