\(A=2+2^2+2^3+...+2^{2020}\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{2021}\)
\(\Rightarrow2A-A=2^{2021}-2\)
\(\Rightarrow A=2^{2021}-2\)
\(\Rightarrow A+2=2^{2021}\)
\(\Rightarrow2\left(A+2\right)=2^{2022}=2^{2.1011}\)
Mà \(2\left(A+2\right)=2^{2x}\)
\(\Rightarrow x=1011\)