a) (1/3)^m = 1/81 b) -512/343 = ( -8/7)^n c) -32/(-2)^n = 4

0 bình luận về “a) (1/3)^m = 1/81 b) -512/343 = ( -8/7)^n c) -32/(-2)^n = 4”

1. Đáp án:

   $\\$

   `a,`

   `(1/3)^m = 1/81`

   `↔ (1/3)^m = (1/3)^4`

   `↔ m = 4`

   Vậy `m=4`

   $\\$

   `b,`

   `(-512)/343 = (-8/7)^n`

   `↔ (-8/7)^3 = (-8/7)^n`

   `↔n=3`

   Vậy `n=3`

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   `c,`

   `(-32)/(-2)^n = 4`

   `↔ -32 = (-2)^n×4`

   `↔ (-2)^n = (-32) ÷ 4`

   `↔ (-2)^n = -8`

   `↔ (-2)^n = (-2)^3`

   `↔ n=3`

   Vậy `n=3`

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   `d,`

   `8/2^n = 4`

   `↔ 8 = 2^n×4`

   `↔2^n=8÷4`

   `↔2^n=2`

   `↔2^n=2^1`

   `↔n=1`

   Vậy `n=1`

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   `e,`

   `(1/2)^{2n-1}=1/8`

   `↔ (1/2)^{2n-1}=(1/2)^3`

   `↔ 2n-1=3`

   `↔2n=3+1`

   `↔2n=4`

   `↔n=4÷2`

   `↔n=2`

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   `f,`

   `1/9 × 27^n = 3^n`

   `↔ 27^n = 3^n ÷ 1/9`

   `↔ (3^3)^n = 3^n × 9`

   `↔ 3^{3n} = 3^n × 3^2`

   `↔ 3^{3n} = 3^{n+2}`

   `↔ 3n = n + 2`

   `↔ 3n – n = 2`

   `↔ 2n = 2`

   `↔n=2÷2`

   `↔n=1`

   Vậy `n=1`

   $\\$

   `g,`

   `1/9 × 3^4 × 3^n = 3^7`

   `↔ 3^4 × 3^n = 3^7 ÷ 1/9`

   `↔ 3^{4 + n}=3^7 × 9`

   `↔ 3^{4 + n} =3^7 × 3^2`

   `↔ 3^{4 + n} = 3^9`

   `↔ 4 + n = 9`

   `↔n=9-4`

   `↔n=5`

   Vậy `n=5`

    

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2. Đáp án:

   a) `(1/3)^m = 1/81`

   `→(1/3)^m = 1^4/3^4`

   `→(1/3)^m = (1/3)^4“

   `→m=4`         

   Vậy `m = 4 `

   b) `-512/343 = ( -8/7)^n`

   `→ {(-8)^3}/7^3 = ( (-8)/7)^n`

   `→ ((-8)/7)^3=( (-8)/7)^n` 

   `→ n = 3`

   Vậy `n=3`

   c) `-32/(-2)^n = 4`

   `→(-2)^5/(-2)^n=(-2)^2`

   `→5-n=2`

   `→n=5-2=3`

   Vậy `n=3`

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