Răspuns:
a) [tex]\bf 2^{61} < 3^{41}[/tex]
b) [tex]\bf 4^{62} < 5^{62}[/tex]
c) [tex]\bf \bf (2^{50}-2^{49}-2^{48})< 3^{32}[/tex]
Explicație pas cu pas:
Salutare!
(a) 2⁶¹ cu 3⁴¹
[tex]\bf 2^{61} = 2\cdot2^{60}=2\cdot(2^{3})^{20}=\boxed{\bf 2\cdot 8^{20}}[/tex]
[tex]\bf 3^{41} = 3\cdot3^{40}=3\cdot(3^{2})^{20}=\boxed{\bf 3\cdot 9^{20}}[/tex]
[tex]\bf 2\cdot 8^{20} < 3\cdot 9 ^{20}[/tex]
[tex]\boxed{\boxed{\bf 2^{61} < 3^{41}}}[/tex]
(b) 2¹²⁴ cu 5⁶²
[tex]\bf 2^{124} = (2^{2})^{62}=\boxed{\bf 4^{62}}[/tex]
[tex]\boxed{\boxed{\bf 4^{62} < 5^{62}}}[/tex]
(c) 2⁵⁰ - 2⁴⁹ - 2⁴⁸ cu 3³²
[tex]\bf 2^{50}-2^{49}-2^{48}=[/tex]
[tex]\bf 2^{48}\cdot(2^{50-48}-2^{49-48}-2^{48-48})=[/tex]
[tex]\bf 2^{48}\cdot(2^{2}-2^{1}-2^{0})=[/tex]
[tex]\bf 2^{48}\cdot(4-2-1)=[/tex]
[tex]\bf 2^{48}\cdot 1= 2^{48} = (2^{3})^{16}=\boxed{\bf 8^{16}}[/tex]
[tex]\bf 3^{32}= (3^{2})^{16}=\boxed{\bf 9^{16}}[/tex]
[tex]\bf 8^{16} < 9 ^{16}[/tex]
[tex]\boxed{\boxed{\bf \bf (2^{50}-2^{49}-2^{48})< 3^{32}}}[/tex]
Retinem: Daca puteri au acelasi exponent, este mai mare puterea care are baza mai mare.
#copaceibrainly
