lean_workbook_plus_18891

Let $3^{k}\;\leq \; 2n+1 \;<\; 3^{k+1}\;$ . Prove that every positive odd integer $m \;\neq\; 3^{k}$ and $3\;\leq \;m \;\leq\;2n+1$ has a power of $3$ strictly smaller than $k\;$ .