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