Question

so sánh lũy thừa

31¹¹ và 17¹⁴

Answer 1

\(31^{11}< 17^{14}\)

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nhae$

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Answer 2

31¹¹ < 32¹¹ = (2⁵)¹¹ = 2⁵⁵

17¹⁴ > 16¹⁴ = (2⁴)¹⁴ = 2⁵⁶

Vì 2⁵⁵ < 2⁵⁶ => 32¹¹ < 16¹⁴ => 31¹¹ < 17¹⁴

Answer 3

Ta có : \(31^{11}< 34^{11}=\left(2.17\right)^{11}=2^{11}.17^{11}\)

Ta đi so sánh \(17^{14}\)và \(2^{11}.17^{11}.\)

ta có : \(17^{14}=17^3.17^{11}.\)Do . \(17^3=4913>2^{11}=2048.\)=> \(17^{14}>2^{11}.17^{11}\)

Vậy : \(31^{11}< 17^{14}\)