a) 5^-1 . 25ⁿ = 125

   1/5 . 25ⁿ = 125

           25ⁿ = 125 : 1/5

           25ⁿ = 625

           25ⁿ = 25²

=> n = 2

a) \(5^{-1}.25^n=125\)

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

\(\Rightarrow25^n=125:\frac{1}{5}\)

\(\Rightarrow25^n=125.5\)

\(\Rightarrow25^n=625\)

\(\Rightarrow25^n=25^2\)

\(\Rightarrow n=2\)

Vậy  n = 2

b) \(3^{-1}.3n+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}+6.3^{n-1}=7.3^6\)

\(\Rightarrow3^{n-1}\left(1+6\right)=7.3^6\)

\(\Rightarrow3^{n-1}.7=7.3^6\)

\(\Rightarrow3^{n-1}=3^6\)

\(\Rightarrow n-1=6\)(vì cùng cơ số 3 > 1)

\(\Rightarrow n=6+1\)

\(\Rightarrow n=7\)

Vậy n = 7

Giải:

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

\(\Leftrightarrow5^{-1}.5^{2n}=125\)

\(\Leftrightarrow5^{2n-1}=5^3\)

\(\Leftrightarrow2n-1=3\)

\(\Leftrightarrow2n=4\)

\(\Leftrightarrow n=2\)

Vậy ...

b) Đề có sai không ạ?

=>3^n+(-1)+6.3^n-1=7.3^6

=>3^n-1+6.3^n-1=7.3^6

=>3^n-1.(1+6)=7.3^6

=>3^n-1.7=7.3^6

=>3^n-1=3^6

=>n-1=6=>n=7

Vậy n=7 tick nhé

\(3^{-1}.3^n+6.3^{n-1}=7.3^6\) dung the nay ko?

dung thi k toi vao giai ko dung cung k roi sua de

7.3⁶

k mình nha các bạn

3\(^{-1}\). 3\(^n\)+ 6.3\(^{n-1}\) =7.3\(^6\)

= 3\(^{-1+n}\)+ 6.3\(^{n-1}\)=7.3\(^6\)

= 3\(^{n-1}\)+ 6.3\(^{n-1}\)=7.3\(^6\)

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

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

n-1=6

n=7

ra bai ngu qua

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