jmc

We want to write everything in terms of powers of 3. Doing so gives us $3^n=3\cdot (3^2{)}^3\cdot (3^4{)}^2$. This simplifies to $3^n=3\cdot 3^6\cdot 3^8$, so $3^n=3^{15}$. Therefore, $n=\boxed{15}$.