\(C=1+3+3^2+...+3^{2013}\)
\(\Rightarrow3C=3+3^2+3^3+...+3^{2014}\)
\(\Rightarrow3C-C=\left(3+3^2+3^3+...+3^{2014}\right)-\left(1+3+3^2+...+2^{2013}\right)\)
\(\Rightarrow2C=3^{2014}-1\)
Mà \(2C+1=3^{2x}\)
\(\Rightarrow3^{2014}-1+1=3^{2x}\)
\(\Rightarrow3^{2014}=3^{2x}\)
\(\Rightarrow2014=2x\)
\(\Rightarrow x=1012\)
Vậy x = 1012