Question

Determinati numerele naturale "n" ,pentru care 6 la puterea n + 6 la puterea n+3= 217 ×6 la puterea 55

Answer 1

$\rm 6^n+6^{n+3}=217 \cdot 6^{55} \\ \\ 6^n(1+6^3)=217 \cdot 6^{55} \\ \\ 6^n (1+216)=217 \cdot 6^{55} \\ \\ 6^n \cdot 217 = 217 \cdot 6^{55 } \Rightarrow 6^n=6^{55} \Rightarrow \boxed{n=55}.$