\(3^{n+2}+3^{n+1}-3^n=891\)
\(3^n\times3^2+3^n\times3-3^n=891\)
\(3^n\times\left(9+3-1\right)=891\)
\(3^n\times11=891\)
\(3^n=891\div11\)
\(3^n=81\)
\(3^n=3^4\)
\(n=4\)
\(3^{n+2}+3^{n+1}-3^n=891\)
\(\Leftrightarrow3^n.3^2+3^n.3-3^n=891\)
\(\Leftrightarrow3^n\left(3^2+3-1\right)=891\)
\(\Leftrightarrow3^n.11=891\)
\(\Leftrightarrow3^n=81\)
\(\Rightarrow n=4\)
\(\Leftrightarrow9.3^n+3.3^n-3^n=891\\ \Leftrightarrow3^n\left(9+3-1\right)=891\\ \Leftrightarrow11.3^n=891\\ \Leftrightarrow3^n=81\\ \Leftrightarrow3^n=3^4\\ \Leftrightarrow n=4\)
