Question

8Tìm n biết:

b) 5^{n + 1} - 2,5ⁿ = 375

Answer 1

Theo đề ta có : 5 \(^{n+1}\) - 2,5\(^n\)= 375

 \(\Rightarrow\)( 2 x 2,5 ) \(^{n+1}\) - 2,5\(^n\)= 375

\(\Rightarrow2^{n+1}.2,5^{n+1}-2,5^n=375\)

\(\Rightarrow2^{n+1}.2,5^n\left(2,5-1\right)=375\)

\(\Rightarrow2^n.2.2,5^n.1,5=375\)

\(\Rightarrow2^n.2,5^n.3=375\)

\(\Rightarrow\left(2.2,5\right)^n=\frac{375}{3}=125\)

\(\Rightarrow5^n=125=5^3\Rightarrow n=3\)

Have a good night,everyone!