Question

So Sánh các số sau :

1, \(3^{54}\) và \(2^{81}\)

2, \(333^{444}\) và \(444^{333}\)

3, \(10^{30}\) và \(2^{100}\)

Answer 1

1. \(3^{54}=\left(3^2\right)^{27}=9^{27}\)

\(2^{81}=\left(2^3\right)^{27}=8^{27}\)

\(\text{Vì }9>8\text{ nên }9^{27}>8^{27}\)

\(\text{Vậy }3^{54}>2^{81}.\)

2. \(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)

\(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)

\(\text{Vì }81^{111}.111^{444}>64^{111}.111^{333}\text{ nên }333^{444}>444^{333}.\)

3. \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

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

Vì 1000 < 1024 nên 1000¹⁰ < 1024¹⁰.

Vậy \(10^{30}<2^{100}.\)

Answer 2

ủng hộ nên 50 điểm nha

Answer 3

bài toan nay kho qua

Answer 4

c) 10^30 = (10^3)^10=1000^10

2^100= (2^10)^10=1024 ^10 

mà 1000<1024 nên : 10^30<2^100

b) A=(3.111)^4.111=(3⁴)¹¹¹.(111⁴)¹¹¹=81¹¹¹.(111⁴⁴⁴

B=(4.111)^3.111=(4³)¹¹¹.(111³)¹¹¹=64¹¹¹.111³³³

81¹¹¹>64¹¹¹; 111⁴⁴⁴>111³³³ => A>B

Answer 5

1/ 3^54 < 2^81

2/ 333^444 > 444^333

3/  10^30 > 2^100

tích nha...^^!!!