Question

comparatil pe 3 la puterea 452 ori 5 cu 5 la puterea 340 repede

Answer 1

[tex]\it 452+4\cdot113 \\\;\\ 340=4\cdot85[/tex]

[tex]\it 3^{113} =3\cdot3^{112} = 3\cdot(3^4)^{28}=3\cdot81^{28} \\\;\\ 5^{85} =5\cdot5^{84} = 5\cdot(5^3)^{28} =5\cdot125^{28}[/tex]

[tex]\it 3\cdot81^{28} \ \textless \ 5\cdot 125^{28} \Rightarrow 3^{113} \ \textless \ 5^{85} \Rightarrow (3^{113})^4 \ \textless \ (5^{85})^4 \Rightarrow \\\;\\ \Rightarrow 3^{452} \ \textless \ 5^{340}[/tex]