Question

[Phạm Vân Anh]

So sánh 

a) 3⁴⁵⁰ và 5³⁰⁰

b) 2³¹ và 3²¹

Answer 1

[Edogawa Conan]

a) Ta có: \(3^{450}=3^{3.150}=\left(3^3\right)^{150}=27^{150}\)

\(5^{300}=5^{2.150}=\left(5^2\right)^{150}=25^{150}\)

Vì 27>25 \(\Rightarrow3^{450}>5^{300}\)

b) \(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10}\)

\(3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)

Vì \(2.8^{10}< 3.9^{10}\Rightarrow2^{31}< 3^{21}\)

\(\)

Answer 2

[Trà My]

a)\(3^{450}=\left(3^3\right)^{150}=27^{150};5^{300}=\left(5^2\right)^{150}=25^{150}\)

27¹⁵⁰>25¹⁵⁰ => 3⁴⁵⁰>5³⁰⁰

b)\(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10};3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)

2<3;8¹⁰<9¹⁰ => 2.8¹⁰<3.9¹⁰ => 2³¹<3²¹