\(A=2+2^2+2^3+...+2^{2020}\)
\(2A=\left(2+2^2+2^3+..+2^{2020}\right).2\)
\(2A=2^2+2^3+2^4+...+2^{2021}\)
\(2A-A=\left(2^2+2^3+2^4+...+2^{2021}\right)-\left(2+2^2+2^3+...+2^{2020}\right)\)
\(A=2^2+2^3+2^4+...+2^{2021}-2-2^2-2^3-...-2^{2020}\)
\(A=\left(2^{2021}-2\right)+\left(2^2-2^2\right)+\left(2^3-2^3\right)+\left(2^4-2^4\right)+...\left(2^{2020}-2^{2020}\right)\)
\(A=2^{2021}-2+0+0+0+...+0\)
\(A=2^{2021}-2\) (1)
Thay (1) vào 2(A+2)=\(2^x\) ta được:
\(2\left(2^{2021}-2+2\right)=2^x\)
\(2\left(2^{2021+0}\right)=2^x\)
\(2.2^{2021}=2^x\)
\(2^{2022}=2^x\)
\(\Rightarrow\)x=2022
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