Question

So sánh:

a) 199²⁰ và 2003¹⁵               b) 3⁹⁹ và 11²¹

c) 5⁴⁰ và 620¹⁰                      d) 3⁴⁸⁴ và 4³⁶³

Answer 1

Ta có :

a) 199²⁰ = ( 1994 )⁵

2003¹⁵ = ( 2003³ )⁵

Vì 199⁴ < 2003³ => ( 199⁴ )5 < ( 2003³ )⁵

=> 199²⁰ < 2003¹⁵

b) 3⁹⁹ = 3³³ )³ 

11²¹ = ( 11⁷ )³

Vì 3³³ > 11⁷

=> ( 3³³ )³ > ( 11⁷ )³

=> 3⁹⁹ > 11²¹

c) Vì 5⁴⁰ = ( 5⁴ )¹⁰ = 625¹⁰ > 620¹⁰

=> 5⁴⁰ > 620¹⁰

d) 3⁴⁸⁴ = ( 3⁴ )¹²¹ = 81¹²¹

4³⁶³ = ( 4³ )¹²¹ = 64¹²¹

Vì 81¹²¹ > 64¹²¹ => 3⁴⁸⁴ > 4³⁶³

Answer 2

So sánh:

\(a)\)\(199^{20}\) và   \(2003^{15}\)

\(\Rightarrow\)\(199^{20}< 200^{20}=\left(2^3.5^2\right)^{20}=2^{60}.5^{40}\)

\(\Rightarrow\)\(2003^{15}>2000^{15}=\left(2.10^3\right)^{15}=\left(2^4.5^3\right)^{15}=2^{60}.5^{45}\)

Vì: \(2^{60}.5^{40}< 2^{60}.5^{45}\)

Nên: \(199^{20}< 2003^{15}\)

\(b)\)\(3^{99}\)và     \(11^{21}\)

\(3^{99}=\left(3^{33}\right)^3\)

\(11^{21}=\left(11^7\right)^3\)

Vì: \(\left(3^{33}\right)^3>\left(11^7\right)^3\)

Nên: \(3^{99}>11^{21}\)

Answer 3

\(c)\)\(5^{40}\)và     \(620^{10}\)

\(\Rightarrow\)\(5^{40}=\left(5^4\right)^{10}=625^{10}>620^{10}\)

\(\Rightarrow\)\(5^{40}>620^{10}\)

\(d)\)\(3^{484}\)và     \(4^{363}\)​

\(\Rightarrow\)\(3^{484}=\left(3^4\right)^{121}=81^{121}\)

\(\Rightarrow\)\(4^{363}=\left(4^3\right)^{121}=64^{121}\)

Vì: \(81^{121}>64^{121}\)

Nên: \(3^{484}>4^{363}\)