Question

so sánh 31^111va 17^139

Answer 1

Ta có : \(31^{11}< 32^{11}=\left(2^5\right)^{111}=2^{555}\)

\(17^{139}>16^{139}=\left(2^4\right)^{139}=2^{556}\)

Vì \(2^{555}< 2^{556}\Rightarrow31^{111}< 17^{139}\)

Vậy \(31^{111}< 17^{139}\)

Answer 2

Ta có: \(31^{111}< 32^{111}\) và \(17^{139}>16^{139}\)

\(\left\{\begin{matrix}32^{111}=\left(2^5\right)^{111}=2^{555}\\16^{139}=\left(2^4\right)^{139}=2^{556}\end{matrix}\right.\)

Vì \(2^{555}< 2^{556}\) nên \(17^{139}>2^{556}>31^{111}\)

\(\Rightarrow17^{139}>31^{111}\)

Vậy: \(17^{139}>31^{111}\)

Answer 3

31/111<17/139