log(x-6) = log x - log 6or, one of my personal favorites,
x ln x = lnI'm at a loss.
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
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2 comments:
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.
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?
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