To illustrate l'Hospital's rule, an AP Calculus BC preparation book has the following:

$\displaystyle \lim_{x \rightarrow 0^+}{x^{\sin x}}=\lim_{x \rightarrow 0^+}{e^{x \ln (\sin x)}}$

Say what? I thought $\displaystyle x^{\sin x}=e^{\sin x \cdot \ln x}$. Is that a typo?

Thanks.