Yes. It's maybe more frequently seen on other functions such as trig functions (e.g. the identity sin²α+cos²α=1) but it crops up a lot on logarithms in computational complexity (as here). I've certainly never seen it used to mean anything else. As grandpa says, base is written as subscript.

The base is usually a subscript: log_2(x), and the square is a superscript, log^2(x).

Example of the superscript notation meaning squared: http://www.springerlink.com/content/7n7219tcyxr81gxc/