a: \(5^{450}=125^{150}\)

\(3^{600}=81^{150}\)

mà 125>81

nên \(5^{450}>3^{600}\)

b: \(3^{450}=\left(3^3\right)^{150}=27^{150}\)

mà 27>5

nên \(3^{450}>5^{150}\)

hay \(3^{453}>5^{150}\)

Câu 1:

(x -5)^4 = (x -5)^6

(x -5)^4 - (x -5)^6 =0

(x -5)^4.(1 - (x -5)^2) = 0

(x -5)= 0 hoặc 1 - (x -5)^2 = 0

TH1:

x - 5 = 0; x = 5

TH2:

1 - (x - 5)^2 = 0

(x -5)^2 = 1

x - 5 = 1 hoặc x - 5 = - 1

x = 6 hoặc x = 4

Vậy x ∈ {4; 5; 6}

Câu 2a:

27^11 và 81^8

A = 27^11 = (3^3)^11 = 3^33

B = 81^8 = (3^4)^8 = 3^32 < 3^33 = A

Vậy A > B

\(a;5^{23}=5\cdot5^{22}< 6\cdot5^{22}\Rightarrow5^{23}< 6\cdot5^{22}\)

\(b;7\cdot2^{13}< 8\cdot2^{13}=2^3\cdot2^{13}=2^{15}\)

\(c;21^{15}=3^{15}\cdot7^{15}>3^{15}\cdot7^{14}=27^5\cdot49^8\)

\(d;199^{20}< 200^{20}=10^{40}\cdot2^{20}< 10^{45}\cdot2^{15}=2000^{15}< 2001^{15}\)

\(e;3^{39}=9^{13}< 11^{13}< 11^{21}\)

khó quá

>

>

a, 2¹⁶ = 2³.2¹³ = 8.2¹³

Vì 7 < 8 => 7.2¹³ < 8.2¹³ => 7.2¹³ < 2¹⁶

b, 21¹⁵ = 3¹⁵.7¹⁵ 

27⁵.49⁸ = 3¹⁵.7¹⁶

Vì 7¹⁵ < 7¹⁶ => 3¹⁵.7¹⁵ < 3¹⁵ < 7¹⁶ => 21¹⁵ < 27⁵ < 49⁸

c, 199²⁰ < 200²⁰ = 8²⁰.25²⁰ = 2⁶⁰.5⁴⁰

2003¹⁵ > 2000¹⁵ = 16¹⁵.125¹⁵ = 2⁶⁰.5⁴⁵

Vì 5⁴⁰ < 5⁴⁵ => 2⁶⁰ . 5⁴⁰ < 2⁶⁰.5⁴⁵ => 199²⁰ < 2003¹⁵

d, 3³⁹ < 3⁴⁰ = (3⁴)¹⁰ = 81¹⁰

11²¹ > 11²⁰ = (11²)¹⁰ = 121¹⁰

Vì 81¹⁰ < 121¹⁰ => 3³⁹ < 11²¹

a) \(7.2^{13}< 8.2^{13}\Rightarrow7.2^{13}< 2^3.2^{13}\Rightarrow7.2^{13}< 2^{16}.\)

a) ta có: 15¹² = 3¹².5¹²

81³.125⁵ = (3⁴)³.(5³)⁵ = 3¹².5¹⁵ > 3¹².5¹²

=> ...

b) ta có: 345² = 345.345 = 342.345 + 345.3

342 .348 = 342.345 + 342.3 < 342.345 + 345.3

=> ...

c) ta có: 3²⁰  = (3² )¹⁰ = 9¹⁰

2³⁰ = (2³)¹⁰ = 8¹⁰

=> ....

d) ta có: 4⁵⁰⁰ = (4⁵)¹⁰⁰ = 1024¹⁰⁰

5⁴⁰⁰ = (5⁴)¹⁰⁰ = 625¹⁰⁰

=> ....

e) ta có: 125⁵ > 108⁵  =27⁵.4⁵ = 27⁵.1024

         27⁷ = 27⁵.27² = 27⁵.729

=> ...