If d is a metric on a (finite dimensional) Banach Space and there exist norms $\|-\|_1$ and $\|-\|_2$ and constants $C_1,C_2 \in [1,\infty)$ satisfying:
\begin{equation} C_1\|x-y\|_1 \leq d(x,y) \leq C_2\|x-y\|_2, \end{equation} then is $d$ normable?
By normable I mean there exists some norm $\|\cdot \|$ such that $\|x,y\|=d(x,y)$.