Question

de comparat 2 la puterea 302 cu 3 la puterea 203​

Answer 1

$\it 2^{302} =2^{2\cdot151}=(2^2)^{101}=4^{151}=4\cdot4^{150}=4\cdot(4^3)^{50}=4\cdot64^{50}\\ \\ 3^{203}=3^{3+200}=3^3\cdot3^{200}=27\cdot3^{4\cdot50}=27\cdot(3^4)^{50}=27\cdot81^{50}\\ \\ 4\cdot64^{50}<27\cdot81^{50} \Rightarrow 2^{302}<3^{203}$

Answer 2

Răspuns:

Explicație pas cu pas:

2³⁰² = 2³⁰⁰ x 2² = (2³)¹⁰⁰ x 4 = 8¹⁰⁰ x 4

3²⁰³ = 3²⁰⁰ x 3³ = (3²)¹⁰⁰ x 27 = 9¹⁰⁰ x 27

=>  8¹⁰⁰ x 4 < 9¹⁰⁰ x 27 pentru ca 8¹⁰⁰ < 9¹⁰⁰, iar 4 < 27

<=>   2³⁰² < 3²⁰³