Ta có: \(2.3^x-405=3^{x-1}\)
\(\Leftrightarrow2.3^x-3^x:3^1=405\)
\(\Leftrightarrow3^x.\left(2-\frac{1}{3}\right)=405\)
\(\Leftrightarrow3^x.\frac{5}{3}=405\)
\(\Leftrightarrow3^x=81.3\)
\(\Leftrightarrow3^x=3^4.3\)
\(\Leftrightarrow3^x=3^5\)
\(\Leftrightarrow x=5\)
Vậy \(x\in\left\{5\right\}\)