Question

[witch roses]

CMR 2¹⁹⁹³<7⁷¹⁴

Answer 1

[giang ho dai ca]

Cách đây nè:

  2^10 = 1025 ; 7^3 = 343 => 2^10 < 3.7^3 => \(\left(2^{10}\right)^{238}<3^{238}.\left(7^3\right)^{238}\)  => 2^2380 < 3^238 .7^714

2^8 = 256 ; 3^5 = 243 => 3^5 < 2^8

Ta có :

  3^328 = 3^3 . 3^325 = \(3^3.\left(3^5\right)^{47}<3^3.\left(2^8\right)^{47}<2^5.2^{376}\Rightarrow3^{328}<2^{381}\)

2^2380 <  2^238 . 7^714  => 2^2380 < 2^238 . 7^714 => 2^1999 < 7^14 mà 2^1999 > 2^1993 => 2^1993 < 7^714

Answer 2

[giang ho dai ca]

Chỉnh lại tý

2^10 = 1025 ; 7^3 = 343 => 2^10 < 3.7^3 => \(\left(2^{10}\right)^{238}<3^{238}.\left(7^3\right)^{238}\)  => 2^2380 < 3^238 .7^714

2^8 = 256 ; 3^5 = 243 => 3^5 < 2^8

Ta có :

  3^328 = 3^3 . 3^325 = \(3^3.\left(3^5\right)^{47}<3^3.\left(2^8\right)^{47}<2^5.2^{376}\Rightarrow3^{328}<2^{381}\)

 2^2380 < 2^238 . 7^714 => 2^1999 < 7^14 mà 2^1999 > 2^1993 => 2^1993 < 7^714