## Wednesday, September 17, 2008

### So Wrong It's Funny

This post is here to serve two purposes. First, I'd like to start recording some of the more comical mistakes I encounter while marking assignments, tests and whatnot. Second, I found something which allows for LaTeX equations to be embedded in a blogger post and I'm testing it out.

Obviously, whenever I post something from an assignment I mark I will not include any names or other identifying information.

The question:
$\mbox{Let }x\mbox{ be a real number. For what values of }x\mbox{ is the identity}\\ \log(x^2)=2\log(x)\\ \mbox{ valid? Explain and justify.}$

$\log(x^2)=2\log(x)\\
\log(x^2)-2\log(x)=0\\
\log(x)(\log(x)-2)=0\\
\mbox{So }\log(x)=0\mbox{ or }\log(x)=2\\
x=1\mbox{ or }x=100$

$\log(x^2)=2\log(x)\\
\log(x)(x)=2\log(x)\\
\log(x)=2\log\\
x=2$

Now, for a little context. The course for which I am marking is intended for first-year university students who want to major in math. The course is designed to teach basic proof techniques, some very elementary number theory, and the basic idea of sets. The professor currently teaching the course is also placing emphasis on communication skills and the ability to express ideas in words as well as equations (something I find astonishingly lacking among most science and engineering undergraduates) and proper, unambiguous use of notation. Clearly she has her work cut out for her, but the reason I bring this up is that these mistakes are only funny (and disheartening) if made by people who should know better; if these same mistakes were made by high school students I would be less likely to find them funny or surprising.

I would also like to add to those of you who feel like you might make similar mistakes: If you are not actually planning to focus on a mathematical area, you have very little reason to know how to properly use logarithms in these kinds of situations. You should not feel bad for not seeing the mistakes above unless you actually should understand the math in question.

On a lighter note, the LaTeX appears to be working quite well.