Question

Comparați numerele 2^302 cu 3^203

Answer 1

$2^{302}=2^{303}:2=(2^3)^{101}:2=8^{101}:2\\ \\ 3^{203}=3^{202}\cdot 3=(3^2)^{101}\cdot 3=9^{101}\cdot 3\\ \\ Observam \ ca:\\ \\ 8^{101}:2< 8^{101} <9^{101}<9^{101}\cdot 3\\ \\ \Rightarrow 2^{302}<3^{203}$

Answer 2

Explicație pas cu pas:

2^302=2^300×2^2=(2^3)^100×4=8^100×4

3^203=3^200×3^3=(3^2)^100×27=9^100×27

8 < 9; 4 < 27 ==> 8^100×4 < 9^100×27

==> 2^302 < 3^203

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