\(2VT=2^{x+1}+2^{x+2}+2^{x+3}+...+...+2^{x+2016}\)
\(VT=2VT-VT=2^{x+2016}-2^x=2^{2016}.2^x+2^x=2^x\left(2^{2016}+1\right)\)
\(VP=2^{2019}-2^3=2^3\left(2^{2016}-1\right)\)
\(\Rightarrow2^2\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\)
\(\Rightarrow2^x=2^3\Rightarrow x=3\)
\(2^x+2^{x+1}+2^{x+2}+2^{x+2015}=2^{2019}-8\left(1\right)\)
Đặt \(S=2^x+2^{x+1}+2^{x+2}+2^{x+2015}\)
\(\Rightarrow S+\left(1+2^2+...2^{x-1}\right)=\left(1+2^2+...2^{x-1}\right)+2^x+2^{x+1}+2^{x+2}+2^{x+2015}\)
\(\Rightarrow S+\dfrac{2^{x-1+1}-1}{2-1}=1+2^2+...2^{x-1}+2^x+2^{x+1}+2^{x+2}+2^{x+2015}\)
\(\Rightarrow S+2^x-1=\dfrac{2^{x+2015+1}-1}{2-1}\)
\(\Rightarrow S+2^x-1=2^{x+2016}-1\)
\(\Rightarrow S=2^{x+2016}-2^x\)
\(\left(1\right)\Rightarrow2^{x+2016}-2^x=2^{2019}-8=2^{2019}-2^3\)
\(\Rightarrow2^x\left(2^{2016}-1\right)=2^3\left(2^{2016}-1\right)\)
\(\Rightarrow2^x=2^3\Rightarrow x=3\)
