The Log Loop - An Amazing Way to Remember How to Convert a Logarithmic Form to Exponential Form

This week in class, one of my colleagues did a Grade 12 (U) lesson on Logarithms - specifically on how to convert logarithmic form to exponential form and vice versa.  I don't know about you, but it's always been quite difficult for me to remember the formula.  My colleague presented an amazing diagram that helps students (and teachers!) remember how it works:

Gruen, Amy. (2011). The Log Loop [drawing]. Retrieved from: http://squarerootofnegativeoneteachmath.blogspot.ca/2011/02/loop-for-logs.html

I love tricks like this!  If you can simply remember that you start at the bottom of the diagram, then you can remember the formula!  So the answer to the above would be:  2^3 = 8   And technically, the loop also works to turn the exponential back into the logarithm.  In the example I just typed, the loop would start with the 2, go around to the 8, then finally to the 3, which would result in the order seen in the picture with the logarithm.  Awesome!

Secondly, my colleague got us all to play "Log War".  It was basically the card game War, but instead of just numbers written on the cards, logarithms were written on the cards.  So, we all had to solve the logarithms in order to find out who had the highest number in the round.  This is an excellent way to get students practicing!

I will say though (as I always do), that I do feel it's important to assign some textbook homework as well, just so the students get used to writing out full solutions like they'd have to on a test.  Giving them homework will also give them a resource to use while studying for the test.

Having said that, I truly enjoyed this lesson and I hope to use it in my classroom someday!