2^x+1.2^2009=2^2010

\(\begin{array}{l}{2^x} + {1.2^{2009}} = {2^{2010}}\\{2^x} + {2^{2009}} = {2^{2010}}\\{2^x} = {2^{2010}} - {2^{2009}}\\{2^x} = {2^{2009}}\left( {2 - 1} \right)\\{2^x} = {2^{2009}}\\ \Rightarrow x = 2009\end{array}\)