Question

Scrieti in ordine crescatoare numerele:a)25¹⁸,125²⁵,5⁴⁰ b)9⁵¹,27⁴⁸,3⁹⁵ c)8¹²,32⁷,27⁸​.

Answer 1

Răspuns:

25 ¹⁸=(5²)¹⁸ =5²ˣ¹⁸=5³⁶

125¹⁵=(5³)¹⁵=5³ˣ⁵=5⁴⁵

5⁴⁰=5⁴⁰

25¹⁸, 5⁴⁰, 125¹⁵

___________

9⁵¹=(3²)⁵¹ =3²ˣ⁵¹=3¹⁰²

27⁴⁸=(3³)⁴⁸=3³ˣ⁴⁸=3¹⁴⁴

3⁹⁵ =3⁹⁵

3⁹⁵, 9⁵¹, 27⁴⁸

__________

8¹²=(2³)¹²=2³ˣ¹²=2³⁶

32⁷=(2⁵)⁷ =2⁵ˣ⁷=2³⁵

27⁸=(3³)⁸=3³ˣ⁸=3²⁴

32⁷, 8¹², 27⁸

Answer 2

Răspuns:

a)

25¹⁸ = (5²)¹⁸ = 5²ₓ¹⁸=5³⁶

125²⁵ = (5³)²⁵ = 5³ₓ²⁵=5⁷⁵

5⁴⁰

⇒ 25¹⁸<5⁴⁰<125²⁵

b)

9⁵¹ = (3²)⁵¹ = 3²ₓ⁵¹ = 3¹⁰²

27⁴⁸ = (3³)⁴⁸ =  3³ₓ⁴⁸ = 3¹⁴⁴

3⁹⁵

⇒ 3⁹⁵ < 9⁵¹ < 27⁴⁸

c)

8¹² = (2³)¹² = 2³ₓ¹² = 2³⁶

32⁷ = (2⁵)⁷ = 2⁵ₓ⁷ = 2³⁵

27⁸ = (3³)⁸ = 3³ₓ⁸ = 3²⁴

⇒ 32⁷  < 8¹²  < 27₈