Question

Daca am 2^113 si trebuie sa il compar cu 7^89 care e mai mare si de ce?

Answer 1

2^113=2•2^112=2•(2^4)^28=2•16^28

7^89=7^5•7^84=7^5•(7^3)^28=7^5•343^28

2<7^5; 16<343

=>2•16^28 < 7^5•343^28

2^113 < 7^89

SAU:

2^113=2^2•2^111=2^2•(2^3)^37=4•8^37

7^89=7^15•7^74=7^15•(7^2)^37=7^15•49^37

4<7^15  si 8<49

4•8^37 < 7^15•49^37

2^113 < 7^89