Question

1. So sanh

A = 3 ^500 B = 7^300

A = 303^202 va B = 202^303

A= 3^21 va B = 2^31

Answer 1

a, A = 3⁵⁰⁰ = (3⁵)¹⁰⁰ = 243¹⁰⁰
B = 7³⁰⁰ = (7³)¹⁰⁰ = 343¹⁰⁰
Mà 243¹⁰⁰ < 343¹⁰⁰
=> A < B
@nguyễn thi trà giang

Answer 2

a) \(A=3^{500}=\left(3^5\right)^{100}=243^{100}\)

\(B=7^{300}=\left(7^3\right)^{100}=343^{100}\)

Vì \(243^{100}< 343^{100}\Rightarrow3^{500}< 7^{300}\)

\(\Rightarrow A< B\)

b) \(A=303^{202}=\left(303^2\right)^{101}=91809^{101}\)

\(B=202^{303}=\left(202^3\right)^{101}=8242408^{101}\)

Vì \(91809^{101}< 8242408^{101}\Rightarrow303^{202}< 202^{303}\)

\(\Rightarrow A< B\)

c) \(A=3^{21}=3\cdot3^{20}=3\cdot\left(3^2\right)^{10}=3\cdot9^{10}\)

\(B=2^{31}=2\cdot2^{30}=2\cdot\left(2^3\right)^{10}=2\cdot8^{10}\)

Ta có: \(3>2;9^{10}>8^{10}\Rightarrow3\cdot9^{10}>2\cdot8^{10}\Rightarrow3^{21}>2^{31}\)

\(\Rightarrow A< B\)