Ta có: \(3^{-1}\cdot3^n+6\cdot3^{n-1}=7\cdot3^6\)
\(\Leftrightarrow3^{n-1}+6\cdot3^{n-1}=7\cdot3^6\)
\(\Leftrightarrow3^{n-1}\cdot\left(1+6\right)=7\cdot3^6\)
\(\Leftrightarrow3^{n-1}\cdot7=3^6\cdot7\)
\(\Leftrightarrow3^{n-1}=3^6\)
\(\Leftrightarrow n-1=6\)
hay n=7
Vậy: n=7