Let $\Psi(x,B)$ denote the number of $B$-smooth numbers less than $x$. Wikipedia gives the following "good estimate" for small, fixed $B$:

$$\Psi(x,B) \sim \frac{1}{\pi(B)!} \prod_{p\le B}\frac{\log x}{\log p}$$

However, no citation or further discussion is given. Where does this estimate come from? How good an estimate is it? Anyone know a reference for this?