I created this page of change of base formula notes for my Algebra 2 students to glue in their interactive notebooks as part of our logarithms unit.
Our end of year standardized test requires students to be familiar with the change of base formula. Last year, I used TI-84 graphing calculators with my students. We had to use the change of base formula in order to evaluate logarithms that were not written with base 10. This year, I am using TI-Nspire graphing calculators with my students. When students press the log button, they are allowed to type in whatever base they choose.
As a class, we brainstormed ways to remember the change of base formula. One student suggested that we think of the a as the attic and the b as the basement. The attic is the top level of a house. The basement is the bottom level of a house. If we are rewriting the log base b of a, the logarithm of the attic ends up on the top of our fraction. The logarithm of the basement ends up on the bottom of our fraction.
Another student suggested that was too complicated. The base of the logarithm is already written lower than the rest of the problem. So, it makes sense for the logarithm of the base to end up on the bottom of the fraction when using the change of base formula.
One other thing that we discussed was natural logarithms with a base of e. We did a short exploration of the number e on our calculators. Next year, I definitely want to spend an extra day on natural logarithms. And, I think we need to create a page regarding natural logarithms for our interactive notebooks.
In 2015, my notes ended up looking quite similar.
More Activities for Teaching Logarithms
- Evaluating Logarithms Auction Activity
- Swap Two – A Logarithms Task
- Exponents Chart (Powers of 2 to 9)
- Earthquakes and Explosions – a Logarithms Problem Based Assessment (PBA)
- Amy Gruen’s Exponent Puzzles
- Solving Logarithmic Equations Foldable
- Converting Between Exponential and Logarithmic Form Foldable
- Logarithm Tarsia Puzzle Activity
- The Case of the Cooling Corpse Task
- Change of Base Formula Notes
- Properties of Logarithms Foldable
- Logarithms Foldable