\(A=3+3^2+ 3^3+...+3^{2011}\)
\(3A=3^2+3^3+3^4+...+3^{2012}\)
\(3A-A=\left(3^2+3^3+3^4+...+3^{2012}\right)-\left(3+3^2+3^3+...+3^{2011}\right)\)
\(2A=3^{2012}-3\)
TA CÓ \(2A+3=3^x\)
Thay \(2A=3^{2012}\) ta được
\(3^{2012}-3+3=3^{2012}\)
\(3^{2012}=3^x\Rightarrow x=2012\)
Vậy \(x=2012\)