Bài `6:`

`a) 5^n + 5^(n+2)=650`

`=> (1+5^2) . 5^n = 650`

`=> (1+25) . 5^n = 650`

`=> 26 . 5^n = 650`

`=> 5^n = 650:26`

`=> 5^n = 25`

`=> 5^n = 5^2`

`=> n=2`

Vậy `n=2`

`b) 2^n + 2^(n+3) =144`

`=> (1+2^3) . 2^n = 144`

`=> (1+8) . 2^n = 144`

`=> 9 . 2^n = 144`

`=> 2^n = 144:9`

`=> 2^n = 16`

`=> 2^n = 2^4`

`=> n=4`

Vậy `n=4`

`c) 8^n : 2^n = 16^2011`

`=> (8:2)^n = 16^2011`

`=> 4^n = 16^2011`

`=> 4^n = (4^2)^2011`

`=> 4^n = 4^4022`

`=> n=4022`

Vậy `n=4022`

`d) 1/9 . 3^4 . 3^n = 3^7`

`=> 1/9 . 81 . 3^n = 3^7`

`=> 9 . 3^n = 3^7`

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

`=> 2+n=7`

`=> n=7-2`

`=> n=5`

Vậy `n=5`

`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) 1/2 . 2^(n+4) . 2^n = 2^5`

`=> 2^(2n+4) = 2^5 : 1/2`

`=> 2^(2n+4) = 32 .2`

`=> 2^(2n+4) =64`

`=> 2^(2n+4)=2^6`

`=> 2n+4=6`

`=> 2n = 6-4`

`=> 2n=2`

`=> n=2:2`

`=> n=1`

Vậy `n=1`