Question

Comparați numerele :
a) 2⁶¹ cu 3⁴¹
b) 2¹²⁴ cu 5⁶²
c) 2⁵⁰ - 2⁴⁹ - 2⁴⁸ cu 3³²​

Answer 1

Răspuns:

a)  $\bf 2^{61} < 3^{41}$

b)  $\bf 4^{62} < 5^{62}$

c)  $\bf \bf (2^{50}-2^{49}-2^{48})< 3^{32}$

Explicație pas cu pas:

Salutare!

(a) 2⁶¹ cu 3⁴¹

$\bf 2^{61} = 2\cdot2^{60}=2\cdot(2^{3})^{20}=\boxed{\bf 2\cdot 8^{20}}$

$\bf 3^{41} = 3\cdot3^{40}=3\cdot(3^{2})^{20}=\boxed{\bf 3\cdot 9^{20}}$

$\bf 2\cdot 8^{20} < 3\cdot 9 ^{20}$

$\boxed{\boxed{\bf 2^{61} < 3^{41}}}$

(b) 2¹²⁴ cu 5⁶²

$\bf 2^{124} = (2^{2})^{62}=\boxed{\bf 4^{62}}$

$\boxed{\boxed{\bf 4^{62} < 5^{62}}}$

(c) 2⁵⁰ - 2⁴⁹ - 2⁴⁸ cu 3³²​

$\bf 2^{50}-2^{49}-2^{48}=$

$\bf 2^{48}\cdot(2^{50-48}-2^{49-48}-2^{48-48})=$

$\bf 2^{48}\cdot(2^{2}-2^{1}-2^{0})=$

$\bf 2^{48}\cdot(4-2-1)=$

$\bf 2^{48}\cdot 1= 2^{48} = (2^{3})^{16}=\boxed{\bf 8^{16}}$

$\bf 3^{32}= (3^{2})^{16}=\boxed{\bf 9^{16}}$

$\bf 8^{16} < 9 ^{16}$

$\boxed{\boxed{\bf \bf (2^{50}-2^{49}-2^{48})< 3^{32}}}$

Retinem: Daca puteri au acelasi exponent, este mai mare puterea care are baza mai mare.

#copaceibrainly

Answer 2

Răspuns:

Explicație pas cu pas: