  We show that for every graph $G$ and every graph $H$ obtained by subdividing
each edge of $G$ at least $O(\log |V(G)|)$, $H$ is nonrepetitively 3-colorable.
In fact, we show that $O(\log \pi'(G))$ subdivisions per edge are enough, where
$\pi'(G)$ is the nonrepetitive chromatic index of $G$. This answers a question
of Wood and improves a similar result of Pezarski and Zmarz that stated the
existence of at least one 3-colorable division with a linear number of
subdivision vertices per edge.
