Đáp án:
$\\$
`a,`
`(1/3)^m = 1/81`
`↔ (1/3)^m = (1/3)^4`
`↔ m=4`
Vậy `m=3`
$\\$
`b,`
`(-512)/343 = (-8/7)^n`
`↔ (-8/7)^3 = (-8/7)^n`
`↔ n=3`
Vậy `n=3`
$\\$
`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`
$\\$
`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`
$\\$
`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`
Vậy `n=2`
$\\$
`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`
$\\$
`h,`
`1/2 × 2^{n+4} × 2^n = 2^5`
`↔ 2^{n+4} × 2^n = 2^5 ÷ 1/2`
`↔ 2^{n+4+n}=2^5×2`
`↔2^{2n+4} = 2^6`
`↔2n+4=6`
`↔2n=6-4`
`↔2n=2`
`↔n=2÷2`
`↔n=1`
Vậy `n=1`
$\\$
`m,`
`8^n ÷ 2^n = 16^{2011}`
`↔ 8^n = 16^{2011} × 2^n`
`↔ (2^3)^n = (2^4)^{2011} × 2^n`
`↔ 2^{3n} = 2^{8044} × 2^n`
`↔ 2^{3n} = 2^{8044 + n}`
`↔ 3n = 8044 + n`
`↔ 3n - n = 8044`
`↔2n=8044`
`↔n=8044÷2`
`↔n=4022`
Vậy `n=4022`
$\\$
`n,`
`2^n + 2^{n + 3} = 144`
`↔ 2^n + 2^n×2^3 = 144`
`↔ 2^n × (1 + 2^3) = 144`
`↔ 2^n × (1 + 8) =144`
`↔ 2^n × 9 = 144`
`↔ 2^n=144 ÷9`
`↔2^n=16`
`↔2^n=2^4`
`↔n=4`
Vậy `n=4`
