Question

Comparaţi: a) 5^8 cu 2¹5 +2·4^7; b) 5^14 cu 3^21.​

Answer 1

Explicație pas cu pas:

a)

2¹⁵ + 2•4⁷ = 2¹⁵ + 2•(2²)⁷ = 2¹⁵ + 2•2¹⁴ = 2¹⁵ + 2¹⁵ = 2•2¹⁵ = 2¹⁶ = (2²)⁸ = 4⁸

5 > 4 => 5⁸ > 4⁸ => 5⁸ > 2¹⁵ + 2•4⁷

b)

5¹⁴ = (5²)⁷ = 25⁷

3²¹ = (3³)⁷ = 27⁷

25 < 27 => 25⁷ < 27⁷ => 5¹⁴ < 3²¹

Answer 2

Răspuns:

2⁵+ 2×4⁷=

2¹⁵+2×(2²)⁷=

2¹⁵+ 2×2¹⁴=

2¹⁵+2¹⁵=

2¹⁵×(1 + 1) =

2¹⁵×2=

2¹⁶= > (2²)⁸ = 4⁸

avem acelasi exponent comparam bazele

5⁸ >  2⁵+2×4⁷

____________

5¹⁴=(5²)⁷= 25⁷

3²¹=(3³)⁷= 27⁷

5¹⁴ < 3²¹