I was sitting in on Ben Hescott’s awesome Theory of Computation class today. He was discussing logarithms with the class, and they were discussing the constant-difference between logarithms. Ben wrote down the following on the board:

I’m not the kind of person to remember that (although I might derive it), but I never want to take the time to do that if I’m in the middle of a calculation.

Here’s how I remember this mid-calculation: your calculator only has one (maybe two) log buttons on it, and I never remember which base the button uses. So, the way I use that button is that I just know to always divide by the log of the base I want, no matter what.

If I want to calculate log₂1024, I just click the log button, then immediately divide by log(2). Even if the base of the log button is 2, it will just divide by log₂2, which just equals 1, so I might have wasted time, but I know I have the correct answer.