Question

Comparati:
2 la puterea 90 si 3 la puterea 54

Vreau toata rezolvarea rapid!

Answer 1

2⁹⁰ ; 3⁵⁴

2⁹⁰ = (2⁵)¹⁸ ; 2⁵ = 32

3⁵⁴ = (3³)¹⁸ ; 3³ = 27

32 > 27 => 2⁹⁰>3⁵⁴

Answer 2

2⁹⁰ si 3⁵⁴ ( cmmdc al 90 si 54 = 9 x 2 = 18 )

90 = 2 x 3² x 5

54 = 2 x 3³

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= > am aflat cmmdc al exponentilor pentru a aduce bazele diferite la acelasi exponent , astfel incat sa le putem compara

2⁹⁰ = ( 2⁵ ) ¹⁸ = 32¹⁸

3⁵⁴= ( 3³ ) ¹⁸ = 27¹⁸

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32¹⁸ > 27¹⁸ == > 2⁹⁰ > 3⁵⁴