log bases

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:

log_conversion

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.