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
