Question

Bài 2: Tìm số nguyên n, biết

a) \(5^{-1}.25^n=125\)

b) \(3^{-1}.3n+6.3^{n-1}=7.3^6\)

Answer 1

a) 5^-1 . 25ⁿ = 125

   1/5 . 25ⁿ = 125

           25ⁿ = 125 : 1/5

           25ⁿ = 625

           25ⁿ = 25²

=> n = 2

Answer 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

Answer 3

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