Question

so sánh 2 lũy thừa 31¹¹ và 17¹⁴

Answer 1

Ta có :

\(31^{11}< 32^{11}=16^{11}.2^{11}\)

\(16^{11}.2^{12}=16^{14}< 17^{14}\)

Lại có :

\(16^{11}.2^{11}< 16^{11}.2^{12}\)

\(\Rightarrow31^{11}< 16^{11}.2^{11}< 16^{11}.2^{12}< 17^{14}\)

\(\Rightarrow31^{11}< 17^{14}\)

Answer 2

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

Answer 3

Ta có:

\(31^{11}< 32^{11}\Leftrightarrow31^{11}< \left(2^5\right)^{11}\Leftrightarrow31^{11}< 2^{55}\left(1\right)\)

\(17^{14}>16^{14}\Leftrightarrow17^{14}>\left(2^4\right)^{14}\Leftrightarrow17^{14}>2^{56}\left(2\right)\)

Từ (1) và (2) ta có:

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

Answer 4

31^11<17^14