## Thursday, October 20, 2016

### What Is It About Logarithms?

I find logarithms to be one of the most interesting topics in the math I teach, along with matrices.  For some reason, though, students freak out about logarithms.  On the test they make the goofiest mistakes, unlike any they've made before (e.g., on quizzes), such as
log(x-6) = log x - log 6
or, one of my personal favorites,
x ln x = ln
I'm at a loss.

Niels Henrik Abel said...

I don't understand how they would come up with your last example. I've seen problems like (ln x)/x being "simplified" to ln because they think they can cancel the variable. They also have a hard time understanding why ln (x/y) (or ln x - ln y) is not the same as (ln x)/(ln y), so I usually throw in some actual values in there and show them what the calculator says. It's funny: they will believe the calculator before they believe me - which is especially difficult when they've keyed in a problem incorrectly and I try to tell them it's wrong ("But this is what my calculator says!").

Drives me crazy.

Darren said...

Dr. Abel:

There was an x on the other side of an equal sign, which the student cancelled in the way I showed. I don't remember exactly what was done, but it was *something* like that.

Another answer I liked (not) was "3 log-base-5". I tell kids that's like putting a square root sign with nothing under it, but when the pressure of a test gets to you, what are you gonna do?