Problem 5.3.32 - Let $\lVert x \rVert_{1}$ and $\lVert x \rVert_{2}$ be norms on the vector space $\mathscr{X}$ such that $\lVert x \rVert_{1}\leq \lVert x \rVert_{2}$. If $\mathscr{X}$ is complete with respect to both norms, then the norms are equivalent.
I know that $0\in \mathscr{X}$ and also I know that the norms are equivalent if there exists a $C_1,C_2 > 0$ such that $$C_1\lVert x \rVert_{1} \leq \lVert x \rVert_{2} \leq C_2\lVert x \rVert_{1}$$ but I am not sure how to show this, any suggestions is greatly appreciated.