Question

Determinați numărul natural n, știind ca: 5^n+5^n+5^n=3^n+3^n+3^n+3^n+3^n

Answer 1

$\it 5^n+5^n+5^n= 3^n+3^n+3^n+3^n+3^n+3^n \Rightarrow3\cdot5^n=5\cdot3^n|_{:(3\cdot5)} \Rightarrow\\ \\ \Rightarrow 5^{n-1}=3^{n-1}|_{:3^{n-1}} \Rightarrow \Big(\dfrac{5}{3}\Big)^{n-1}=1 \Rightarrow n-1=0 \Rightarrow n=1$