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

a)5^-1*5ⁿ=125

5^-1+n=5³

=>-1+n=3

n=3+1

n=4

b)3^-1*3ⁿ+6*3^n-1=7*3⁶

3^n-1+6*3^n-1=3⁶*7

3^n-1(1+6)=7*3⁶

3^n-1*7=7*3⁶

=>n-1=6

n=6+1

n=7

c)3⁴<1/9*27ⁿ<3¹⁰

3⁴<3^-2*3³ⁿ<3¹⁰

3⁴<3^3n-2<3¹⁰

=>4<3n-2<10

6<3n<12

2<n<4

n=3

d)25<5ⁿ/5<625

5²<5^n-1<5⁴

=>2<n-1<4

3<n<5

n=4

(nể tình bạn nên làm hết ln, nếu cậu k phải bn tớ thì tớ làm dc 2,3 câu xong tương tự r)

cam n ban

Tao làm ***** biết làm . Tự làm đi con ***** xàm lồn.

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

\(3^{-1}.3^n+6.3^{n-1}=7.3^6\Leftrightarrow\frac{3^n}{3}+\frac{6.3^n}{3}=\frac{7.3^7}{3}\) sua 3n=3^n phù hợp

\(3^n+6.3^n=7.3^7\Leftrightarrow7.3^n=7.3^7\)=>n=7