In LaTeX the command is \log, ans I presume our latex engine supports this: \log; this this is maths, all logs in mathematics are to base e with the exception of people doing entropy/computing/information theory who use base 2, but would still use log since the usage makes clear that they are in base 2 (no that isn't supposed to start a debate or a flame war, it is a simple observation of the standard notation in higher level maths i.e. NOT what you were told in calc 101).
I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr:
$$
\mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}}
$$