Bài 1 Tìm STN n , biết a,8.$2^{n}$ =128 b,121.$11^{n}$ = 1331 c,9 < $3^{n}$ : 3 < 81 d,$5^{n}$ .$5^{n+1}$ .$5^{n+2}$ < $2^{10}$ . $^{18}$ : $2^{18}$

0 bình luận về “Bài 1 Tìm STN n , biết a,8.$2^{n}$ =128 b,121.$11^{n}$ = 1331 c,9 < $3^{n}$ : 3 < 81 d,$5^{n}$ .$5^{n+1}$ .$5^{n+2}$ < $2^{10}$ . $^{18}$ : $2^{18}$”

1. `Answer:`

   `a,8.2^n =128`

   `=> 2^3 . 2^n = 2^7`

   `=> 2^n = 2^7 : 2^3 = 2^4`

   `=> n = 4`

   `b, 121 . 11^n = 1331`

   `=> 11^2 . 11^n = 11^3`

   `=> 11^n = 11^3:11^2 = 11^1` 

   `=> n =1`

   `c, 9<3^n:3<81`

   `=> 3^2 < 3^(n-1) < 3^4`

   `=> 2< n-1<4`

   `=> n-1 = 3`

   `=> n = 4`

   `d, 5^n .5^n+1 . 5^n+2 < 2^10 . 2^18 `

   `5^(3n+3) < 2^10 `

   `5^(3n+3) < 1024`

   `3n+3 ∈ { 1,2,3,4}`

   `=> 3(n+1) ∈ {1,2,3,4}`

   Để `n ∈ N `

   `=> 3(n+1) = 3`

   `=> n+1 = 1`

   `=> n=0`

   `Go od luck !`

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2. `a) 8 . 2^n = 128`

   `=> 2^n = 128 : 8`

   `=> 2^n = 16`

   `=> 2^n = 2^4`

   `=> n = 4.`

   `b) 121 . 11^n = 1331`

   `=> 11^n = 1331 : 121`

   `=> 11^n = 11`

   `=> n = 1.`

   `c) 9 < 3^n : 3 < 81`

   `=> 3^2 < `$3^{n – 1}$` < 3^4`

   `=> n – 1 = 3`

   `=> n = 3 + 1 = 4.`

   `d) 5^n . `$5^{n + 1}$` . `$5^{n + 2}$` < 2^10 . 2^18 : 2^18`

   `=> `$5^{3n + 3}$` < 2^10`

   `=> `$5^{3n + 3}$` < 1024`

   `=> 3n + 3 ∈ {1;2;3;4}`

   `=> 3(n + 1) ∈ {1;2;3;4}`

   Để n là STN => 3(n + 1) phải chia hết cho 3

   `=> 3(n + 1) = 3`

   `=> n + 1 = 1`

   `=> n = 1 – 1 = 0.`

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