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2¹⁰⁰và 10³⁰

2¹⁰⁰=2^10.10=(2¹⁰)¹⁰=1024¹⁰

 10³⁰=10^3.10=(10³)¹⁰=1000¹⁰

1024 > 1000

=>1024¹⁰ > 1000¹⁰

=>2¹⁰⁰>10³⁰ 

Ta có : 

2¹⁰⁰ = (2⁵)²⁰ = 32²⁰

Vì 32 > 10 nên 32²⁰ > 10²⁰ hay 10²⁰ < 2¹⁰⁰

Ủng hộ mk nha !!! ^_^

2¹⁰⁰ = (2⁵)²⁰ = 32²⁰ > 10²⁰

=> 2¹⁰⁰ > 10²⁰

\(10^{20}=10^{2^{10}}=100^{10}\)

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

mà 100^10 < 1024^10 

=> 10^20 < 2^100

\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{100^2}< \frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=\)

\(=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{100-99}{99.100}=\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}< 1\)

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

2^100=(2^10)^10=1024^10

1024>1000 nên 1024^10>1000^10

Vậy 2^100>10^30

Ta có 10^30=(10^3)^10=1000^10

Ta có 2^100=(2^10)^10=1024^10

Vì 1000 < 1024 => 1000^10 < 1024^10

=> 10^30 < 2^100 

Vậy 10^30 < 2^100

Nếu thấy đúng k mk nha....

So sánh:10³⁰ và 2¹⁰⁰

Ta có:10³⁰=(10³)¹⁰=1000¹⁰

2¹⁰⁰=(2¹⁰)¹⁰=1024¹⁰

Vì 1000¹⁰<1024¹⁰ nên 10³⁰<2¹⁰⁰

2^100 
= 2^31 . 2^69 
= 2^31 . 2^63 . 2^6 
= 2^31 . (2^9)^7 . (2^2)^3 
= 2^31 . 512^7 . 4^3 (1) 
10^31 
= 2^31 . 5^31 
= 2^31 . 5^28 . 5^3 
= 2^31 . (5^4)^7 . 5^3 
= 2^31 . 625^7 . 5^3 (2) 
Từ (1) và (2), ta có: 
2^31 . 512^7 . 4^3 < 2^31 . 312^7 . 5^3 < 2^31 . 625^7 . 5^3. 
Hay 2^100 < 10^31.

2^100 < 10^31

10³¹    >     2¹⁰⁰

\(10^{30}vs\)\(2^{100}\)

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

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

Vì \(1000^{10}< 1024^{10}=>10^{30}< 2^{100}\)

\(3^{54}vs2^{81}\)

\(3^{54}=\left(3^6\right)^9=729^9\)

\(2^{81}=\left(2^9\right)^9=512^9\)

Vì \(729^9>512^9=>3^{54}>2^{81}\)

\(3^{200}=\left(3^2\right)^{100}=9^{100}\)

\(2^{300}=\left(2^3\right)^{100}=8^{100}\)

Vì \(8^{100}< 9^{100}=>2^{300}< 3^{200}\)