Quantitative Skills > Teaching Methods > Teaching Quantitative Literacy > Logarithms

Geologic context:
earthquakes, floods and flooding, grain sizes/sedimentology, radioactive decay, population growth, changes in atmospheric CO2, decibel scale, pH scale

Teaching logarithms (logs)

by Dr. Eric M. Baer, Geology Program, Highline Community College
Jump down to: Teaching strategies | Materials & Exercises | Student Resources

Logarithms are the inverse of the exponential function. Originally developed as a way to convert multiplication and division problems to addition and subtraction problems before the invention of calculators, logarithms are now used to solve exponential equations and to deal with numbers that extend from very large to small in a more elegant fashion. For more information on exponential functions, go to the Exponential Growth and Decay page.

The logarithm function (log) is defined by
y=logb(x) if and only if x=by
and x>0, b>0 and b not equal to 1.
The function is read and is read "y is the log base b of x"

When no base (b) is noted, the assumed base is 10. Thus,
y=log(x) is the same as y=log10(x)
When the base is the number e (~2.71...), the logarithmic function is called the "natural logarithm" and notated as ln. Thus,
y=loge(x) is written y=ln(x)
There are some properties of logarithmic functions that may be helpful for solving problems with logs.
  • logbbx = x
  • logbb = 1
  • logb1 = 0
  • blogbX = X

Teaching Strategies: Ideas from Math Education

Put quantitative concepts in context


There are a number of geologic contexts in which logs are used and can be introduced. Some of these include:

Use multiple representations


Because everyone has different ways of learning, mathematicians have defined a number of ways that quantitative concepts can be represented to individuals. In the geosciences, logarithms are most commonly represented graphically.

Use technology appropriately


Students have any number of technological tools that they can use to better understand quantitative concepts -- from the calculators in their backpacks to the computers in their dorm rooms. Logarithms can make use of these tools to help the students understand this often difficult concept.


Work in groups to do multiple day, in-depth problems


Mathematicians also indicate that students learn quantitative concepts better when they work in groups and revisit a concept on more than one day. Therefore, when discussing quantitative concepts in entry-level geoscience courses, have students discuss or practice the concepts together. Also, make sure that you either include problems that may be extended over more than one class period or revisit the concept on numerous occasions. Logarithms are a concept that comes up over and over in introductory geoscience: radioactive decay, Richter magnitude, pH scale, etc. When each new topic is introduced, make sure to point out that they have seen this type of function before and should recognize it.

Teaching Materials and Exercises

Student resources


« Previous Page      Next Page »