hay- tích đi

a) 5^23 và 6 . 5^22

Ta có: 5^23 = 5^22 . 5

Vì 5 < 6 nên 5^23 < 6 . 5^22

b) 7 . 2^13 và 2^16

Ta có: 2^16 = 2^13 . 2^3 = 2^13 . 8

Vì 7 < 8 nên 7 . 2^13 < 2^16

c) 21^15 và 27^5 . 49^8

Ta có: 21^15 = (3.7)^15 = 3^15 . 7^15

27^5 . 49^8 = (3^3)^5 . (7^2)^8 = 3^15 . 7^16

Vì 7^15 < 7^16 nên 21^15 < 27^5 . 49^8

f

a) (49⁵ . 7¹⁶) : (7¹⁸.7⁶)

=((7²)⁵.7¹⁶) :7²⁴

=(7¹⁰.7¹⁶) :7²⁴

=7²⁶ : 7²⁴=7²=49

b) (4¹⁶.8²⁰ ) : (2¹⁴.32¹⁵)

=((2²)¹⁶.(2³)²⁰) : (2¹⁴.(2⁵)¹⁵

=(2³².2⁶⁰) : (2¹⁴.2⁷⁵)

=2⁹² : 2⁸⁹=2³=8

Câu 1.99²⁰và 9999¹⁰

⁼(99²)¹⁰=9801¹⁰

Vậy 9801¹⁰<9999¹⁰ suy ra  99²⁰<9999¹⁰

Câu 2. 3⁵⁰⁰và 7³⁰⁰

 3⁵⁰⁰=(3⁵)¹⁰⁰=243¹⁰⁰

7³⁰⁰=(7³)¹⁰⁰=343¹⁰⁰

Vậy 243¹⁰⁰<343¹⁰⁰ => 3⁵⁰⁰<7³⁰⁰

\(2^{x-3}=128\Leftrightarrow2^{x-3}=2^7\Rightarrow x-3=7\Leftrightarrow x=10\)

\(\left(x+6\right)^4=4096\Leftrightarrow\left(x+6\right)^4=2^{12}=\left(2^3\right)^4=8^4\Rightarrow x+6=8\Leftrightarrow x=2\)

\(2^{2018}=\left(2^4\right)^{504}.2^2==16^{504}.4< 16^{900}\\ \)

\(17^{20}>16^{20}=\left(4^2\right)^{20}=4^{40}\)

\(3^{444}=\left(3^4\right)^{111}=81^{111}>64^{111}=\left(4^3\right)^{111}=4^{333}\\ \)

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