Question

Comparati numerele:
x = 3^542 - 3^541 - 3^540
y = 5^361

Answer 1

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