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Change of Base Formula Notes

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.

logarithm change of base formula for algebra 2 interactive notebook logs unit

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.

logarithm change of base formula for algebra 2 interactive notebook logs unit

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.

logarithm change of base formula notes.
logarithm change of base formula notes.


Saturday 2nd of December 2017



Wednesday 19th of April 2017

Thank you!


Thursday 18th of June 2015

Thank you! I'm teaching Algebra 2 this summer for the first time in years. I so appreciate the resources and your descriptions for this unit!

Sarah Carter (@mathequalslove)

Monday 22nd of June 2015

You're welcome, Rachel! Thanks for reading my blog!


Friday 12th of June 2015

If you download the new OS for the TI84, you can find the LogBASE function in a "mathtype" friendly form by pressing ALPHA and F2(WINDOW).

Sarah Carter (@mathequalslove)

Monday 15th of June 2015

Thanks Monica!


Wednesday 5th of February 2014

First of all, I love everything I have found on your blog! It is very helpful to for new Algebra II teachers. But I did want to let you know that there is a way to do logs with different bases on the TI-84. You have to look in the MATH menu, I believe it is option A: LogBASE( But that's awesome you have Nspires this year!

Sarah Carter (@mathequalslove)

Monday 10th of February 2014

Thanks for your sweet comment! And, I'm excited to find out about this new TI-84 option! Oklahoma has yet to decide if Nspires will be allowed on next year's state test, so I may have to go back to using the 84. It's a good thing I love them both! Thanks for sharing!

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