[tex]\text{Folosim formula: } \\
2^0+2^1+2^2+2^3+2^4+\cdots+2^n=2^{n+1} -1\\
\text{Echivalenta cu:}\\
1+2+2^2+2^3+2^4+\cdots+2^n=2^{n+1}-1\\\\
\text{In enuntul tau nu avem primul termen (1) din formula generala.}\\
\text{Din acest motiv, rezultatul va fi cu 1 mai mic.}\\\\
\text{Rezolvare:}\\\\
2+2^{2}+2^{3}+2^{4}+...+2^{x}=2^{55}-2\\\\
2+2^{2}+2^{3}+2^{4}+...+2^{x}=2^{x+1}-1-1\\\\
2^{x+1}-1-1= 2^{55}-2\\\\
2^{x+1}-2=2^{55}-2\\
2^{x+1}=2^{55}\\
x+1=55 \\
x=55-1=\boxed{54} [/tex]
