Question

So sánh : 

\(31^{11}\) và \(17^{14}\)

Answer 1

\(31^{11}\)và \(17^{14}\)

Ta có :

\(31^{11}< 32^{11}=\left(4.8\right)^{11}=4^{11}.8^{11}=2^{22}.8^{11}\)

\(17^{14}>16^{14}=2^{14}.8^{14}=2^{14}.8^3.8^{11}=2^{14}.2^9.8^{11}=2^{23}.8^{11}\)

Ta có : \(2^{23}.8^{11}>2^{22}.8^{11}\), nên \(16^{14}>32^{11}\)

Vậy \(17^{14}>16^{14}>32^{11}>31^{11}\Rightarrow17^{14}>31^{11}\)

Answer 2

Ta có : 31¹¹ < 32¹¹ = (2⁵)¹¹= 2⁵⁵

               17¹⁴ > 16¹⁴ = (2⁴)¹⁴= 2⁵⁶

Vì 2⁵⁵ < 2⁵⁶

=>31¹¹<17¹⁴

Answer 3

Ta có:    
và  
mà  
nên  
Vậy