2^1993>7^714

      \(2^{10}=1024< 1029=3.7^3\)

\(\Leftrightarrow\left(2^{10}\right)^{238}< \left(3.7^3\right)^{238}\)

\(\Leftrightarrow2^{2380}< 3^{238}.7^{714}\) \(\left(1\right)\)

      \(3^5=243< 256=2^8\) \(\left(2\right)\)

      \(3^3=27< 32=2^5\) \(\left(3\right)\)

      Từ \(\left(2\right)\), \(\left(3\right)\) ta có:

      \(3^{328}=3^3.3^{325}=3^3\left(3^5\right)^{47}< 2^5\left(2^8\right)^{47}=2^{381}\)\(\left(4\right)\)

      Từ \(\left(1\right)\), \(\left(4\right)\) ta có:

      \(2^{2380}< 3^{238}.7^{714}\)

\(\Leftrightarrow2^{2380}< 2^{381}.7^{714}\)

\(\Leftrightarrow2^{1999}< 7^{714}\)

\(\Leftrightarrow2^{1993}< 7^{714}\).

\(2^{10}=1024< 1025;7^3=343\Rightarrow2^{10}< 1025< 1029=3.7^3\)

\(\Rightarrow\left(2^{10}\right)^{238}< \left(3.7^3\right)^{238}\Leftrightarrow2^{2380}< 3^{238}.7^{714}\)

\(2^8=256;3^5=243\Rightarrow2^8>3^5\)

\(3^{328}=3^3.3^{325}=3^3.\left(3^5\right)^{47}< 3^3.\left(2^8\right)^{47}< 2^5.2^{376}=2^{381}\)\(\Rightarrow3^{328}< 2^{381}\)

\(2^{2380}< 3^{238}.7^{714}\Rightarrow2^{1999}< 7^{714}\Leftrightarrow2^{1993}< 7^{714}.\)

Mình xin trả lời:

2¹² =1025; 7³ =343 => 2¹⁰ < 3.7³ => (2¹⁰)²³⁸  <3²³⁸ .(7³)²³⁸ => 2²³⁸⁰< 3²³⁸ . 7⁷¹⁴

2⁸= 256; 3⁴ =243=> 3⁵ < 2⁸ 

Ta có : 3²³⁸= 3³. 2²²⁵ = 3³. (3⁵) ⁴⁷ < 2⁵. 2³⁷⁶ => 3³²⁸ < 2³⁸¹

2²³⁸⁰ < 2²³⁸ . 7⁷¹⁴ => 2¹⁹⁹⁹ < 714 mà 2¹⁹⁹⁹> 2¹⁹⁹³ => 2¹⁹⁹³< 7⁷¹⁴

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Cách đây nè:

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

Chỉnh lại tý

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

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