This is nothing earth-shattering, but I feel my Algebra 2 students are less freaked out by logarithms this year, and I think it has to do with how I first introduced them. I used to start by declaring A LOGARITHM IS AN EXPONENT, like saying it loudly and slowly would help it sink in better. I should really know better by now. Well ok maybe, I do know better by now, because this year I started by inviting them to play a fun puzzle:
(Adapted from James Tanton's monthly St. Mark's Math Institute newsletter.)
And then let them in on the dirty little trick that in math we insist on calling it a logarithm instead of a power when we write it like that.
To answer the inevitable "What the hell?", I go into a little history of how John Napier invented logarithms to make multi-digit multiplication easier for Renaissance astronomers.
Then we mention that it's an inverse of an exponential equation, play a little more with shifting between exponential equations and log equations, and we are done for the day.
Here are my filled in notes:
smart notebook file. Here is a google doc with text of a task for easy copy and pasting.