How many positive [integers](https://artofproblemsolving.com/wiki/index.php/Integer) $b$ have the property that $\log_{b} 729$ is a positive integer?
$\mathrm{(A) \ 0 } \qquad \mathrm{(B) \ 1 } \qquad \mathrm{(C) \ 2 } \qquad \mathrm{(D) \ 3 } \qquad \mathrm{(E) \ 4 }$
If $\log_{b} 729 = n$, then $b^n = 729$. Since $729 = 3^6$, $b$ must be $3$ to some [factor](https://artofproblemsolving.com/wiki/index.php/Factor) of 6. Thus, there are four (3, 9, 27, 729) possible values of $b \Longrightarrow \boxed{\mathrm{E}}$.