X-31=5 NGŨ 2

ngũ hay mũ thế bn?

31¹¹<32¹¹=(2⁵)¹¹=2⁵⁵

17¹⁴>16¹⁴=(2⁴)¹⁴=2⁵⁶

vì 2⁵⁵<2⁵⁶ => 32¹¹<16¹⁴

=>31¹¹<17¹⁴

\(31^{11}<32^{11}=\left(2^5\right)^{11}=2^{55}\)

\(17^{14}>16^{14}=\left(2^4\right)^{14}=2^{56}\)

\(31^{11}<32^{11}<16^{14}<17^{14}\)

=> \(31^{11}<17^{14}\)

Cac bạn chỉ cần ghi kết quả thôi nhé

31 mũ 11 < 32 mũ 11 = 16 mũ 11 x 2 mũ 11 
17 mũ 14 > 16 mũ 14 = 16 mũ 11 x 16 mũ 3 = 16 mũ 11 x 2 mũ 12 > 16 mũ1..
Vậy 31 mũ 17 < 17 mũ 14 
 Bài toán là vậy đó. 

TA có: \(A=\frac{20^{10}+1}{20^{10}-1}=\frac{20^{10}-1+2}{20^{10}-1}=1+\frac{2}{20^{10}-1}\)

\(B=\frac{20^{10}-1}{20^{10}-3}=\frac{20^{10}-3+2}{20^{10}-3}=1+\frac{2}{20^{10}-3}\)

TA có: \(20^{10}-1>20^{10}-3\)

=>\(\frac{2}{20^{10}-1}<\frac{2}{20^{10}-3}\)

=>\(\frac{2}{20^{10}-1}+1<\frac{2}{20^{10}-3}+1\)

=>A<B

31¹¹<32¹¹=(2⁵)¹¹=2⁵⁵

=>31¹¹<2⁵⁵

17¹⁴>16¹⁴=(2⁴)¹⁴=2⁵⁶

17¹⁴>2⁵⁶

vì 2⁵⁵<2⁵⁶ nên

31¹¹<2⁵⁵<2⁵⁶<17¹⁴

vậy 31¹¹<17¹⁴

So sanh:

31¹¹ va 17¹⁴

a)17¹⁴>16^14₌2⁵⁶>32¹¹=2²²>31¹¹

b)1023³⁰<1024³⁰=2³⁰⁰<2³⁰⁵=32⁶¹<33⁶¹

c)82¹⁷>81¹⁷=3⁶⁸>3⁶³=27²¹>26²¹

d)3³⁹<3⁴²=9²¹<11²¹

2^48 = (2^3)^16 = 8^16 

8^16 < 8^17 

Vậy 2^48 < 8^17 

35.6^3 = 7.5.6^3 

7^5 = 7.7.7^3 

7.5.6^3 < 7.7.7^3 

Vậy 35.6^3 < 7^5