[tex]x=3^{542}-3^{541}-3^{540}=3^{540}(3^{2}-3-1)=3^{540}(9-3-1)=3^{540}*5 \\ y=5^{361}[/tex]
Avem de comparat: [tex]3^{540}*5[/tex] si [tex]5^{361}[/tex].
Adica avem de comparat: [tex]3^{540}[/tex] si [tex]5^{360}[/tex]
[tex]3^{540}=(3^{3})^{180}=27^{180} \\ 5^{360}=(5^{2})^{180}=25^{180[/tex]
[tex]27^{180}\ \textgreater \ 25^{180}[/tex]
deoarece exponentii sunt egali si doar baza e mai mare (27>25)
deci:
[tex]3^{540}*5\ \textgreater \ 5^{361}[/tex]
deci:
[tex]x\ \textgreater \ y[/tex]
