Question

So sánh các số sau ,số nào lớn hơn:

a, 10³⁰ và 2¹⁰⁰

b, 333⁴⁴⁴ và 444³³³

c,13⁴⁰ và 2¹⁶¹

d,5³⁰⁰ và 3⁴⁵³

Answer 1

a, 2^100

b, 333^444

c,2^161

d, 3^453

Answer 2

a) Ta có : \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

                  \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

mà \(1000< 1024\)

\(\Rightarrow1000^{10}< 1024^{10}\)

\(\Rightarrow10^{30}< 2^{100}\)

b) Ta có : \(333^{444}=\left(111.3\right)^{444}=111^{444}.3^{444}=111^{444}.\left(3^4\right)^{111}=111^{444}.81^{111}\)

                 \(444^{333}=\left(111.4\right)^{333}=111^{333}.4^{333}=111^{333}.\left(4^3\right)^{111}=111^{333}.64^{111}\)

mà \(444>333\Rightarrow111^{444}>111^{333}\)

và \(81>64\Rightarrow81^{111}>64^{111}\)

\(\Rightarrow111^{444}.81^{111}>111^{333}.64^{111}\)

\(\Rightarrow333^{444}>444^{333}\)

c) Ta có : \(2^{161}>2^{160}=\left(2^4\right)^{40}=16^{40}>13^{40}\)

\(\Rightarrow2^{161}>13^{40}\)

d) Ta có : \(3^{453}>3^{450}=\left(3^3\right)^{150}=27^{150}>25^{150}=\left(5^2\right)^{150}=5^{300}\)

\(\Rightarrow3^{453}>5^{300}\)