When simplified, $\log{8} \div \log{\frac{1}{8}}$ becomes:
$\textbf{(A)}\ 6\log{2} \qquad \textbf{(B)}\ \log{2} \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 0\qquad \textbf{(E)}\ -1$
First, note that $\frac{1}{8} = 8^{-1}$.  That means the expression can be rewritten as
\[\log{8} \div \log{8^{-1}}\]
\[\log{8} \cdot \frac{1}{\log{8^{-1}}}\]
\[\log{8} \cdot \frac{1}{-1 \cdot \log{8}}\]
This simplifies to $-1$, which is answer choice $\boxed{\textbf{(E)}}$.