Question

Chứng minh rằng: 2¹⁹⁹³ < 7⁷¹⁴

Answer 1

Ta có 7 mũ 714 > 2 mũ 1993

=> 2 mũ 1993 < 7 mũ 714

Answer 2

2¹² = 1025 ; 7³ = 343 \(\Rightarrow\) 2¹⁰ < 3.7³ \(\Rightarrow\)\(\left(2^{10}\right)^{238}< 3^{238}.\left(7^3\right)^{238}\)\(\Rightarrow\)2²³⁸⁰ < 3²³⁸.7⁷¹⁴ .

2⁸ = 256 ; 3⁴ = 243 => 3⁵ < 2^8

Ta có : 3³²⁸ = 3³.2²²⁵ = \(3^3.\left(3^5\right)^{47}< 3^3.\left(2^8\right)^{47}< 2^5.2^{376}\Rightarrow3^{328}< 2^{381}\)

2²³⁸⁰ < 2²³⁸.7⁷¹⁴ => 2²³⁸⁰ < 2²³⁸.7⁷¹⁴ => 2¹⁹⁹⁹ < 714 mà 2¹⁹⁹⁹ > 2¹⁹⁹³ => 2¹⁹⁹³ < 7⁷¹⁴ .

Answer 3

\(^{2^{12}}\)=4096 mà ???????????????????????????????