25 < 5^n+1 < 125 

=> 5^2 < 5^n+1 <5^3 

=> 2 < n + 1 < 3 

=> 2 - 1 < n < 3 - 1

=>  1 < n < 2 

Vậy 1< n < 2 

5 ^{- 1}  . 25 ⁿ = 125

=> 25 ⁿ = 125 : 5 ^{- 1}

=> 25 ⁿ = 625

=> 25 ⁿ = 25 ²

=> n = 2

5+ 5 + 5 + 5+ 5 + 5 +5+ 5 + 5 +5=5x10=50

25 + 25 + 25 + 25 + 25 + 25 +25 + 25=25x8=200

45 + 45 + 45 + 45 + 15 + 15 + 15 + 15=(45x4)+(15x4)=180+60=240

5+ 5 + 5 + 5+ 5 + 5 +5+ 5 + 5 +5
= 5 x 10
= 50

25 + 25 + 25 + 25 + 25 + 25 +25 + 25
= 25 x 8
= 200

45 + 45 + 45 + 45 + 15 + 15 + 15 + 15
= 45 x 4 + 15 x 4
= 180 + 60
= 240

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18
= (2 + 18) + (4 + 16) + (8 + 12) + (6 + 14) + 10
= 20 + 20 + 20 + 20 + 10 
= 20 x 4 + 10
= 80 + 10
= 90 

125 + 125 + 125 + 125 - 25 - 25 - 25 - 25 
= 4 x (125 - 25) 
= 4 x 100 
= 400
(Tick cho mk pls ^^)

n cũng là -1 ta có :

5^-1=-5

25^-1=-25

-5x-25=125

5^-1 .  25ⁿ = 125

=> 5^-1 . 5²ⁿ = 5³

=> -1 + 2n = 3

=> 2n = 4

=> n = 2

5^-1 .  25ⁿ = 125

=> 5^-1 . 5²ⁿ = 5³

=> -1 + 2n = 3

=> 2n = 4

=> n = 2

\(=>5^2<5^{n-1}<5^3=>n\in\varphi\)

a, 5\(^{-1}\)25\(^n\)=125

\(\frac{1}{5}\)25\(^n\)=125

25\(^n\)=625

n=2

b, 3\(^{-1}\)3\(^n\)+6. 3\(^{n-1}\)=7.3\(^6\)

3\(^{n-1}\)+6. 3\(^{n-1}\)=7.3\(^6\)

3\(^{n-1}\)(6+1)=7.3\(^6\)=3\(^{n-1}\).7

3\(^6\)=3\(^{n-1}\)

6=n-1

n=7

c,3\(^4\)<1/9.27^n <3^10

3^4<1/(3^2) .3^(3n)<3^10

3^4<3^(3n-2)<3^10

3n-2 chia 3 dư 1 nên 3n-2 = 7

n=3

d,25<5^n:5<625

5^2<5^(n-1)<5^4

n-1=3 nên n=4