Ta có: 104²⁰¹⁵ + 2 < 104²⁰¹⁶ + 2.

=> A = \(\frac{104^{2015}+2}{104^{2016}+2}\)< 1 (1).

Ta có: 104²⁰¹⁶ + 2 > 104²⁰ + 2 > 104²⁰.

=> B = \(\frac{104^{2016}+2}{104^{20}}\) > 1 (2).

Từ (1) và (2) => A < 1 < B => A < B.

Chúc bạn học tốt nhé!

bạn ơi giúp mình sửa mẫu của B thành 104^2017+2 nhé

Thanks bạn nhìu

2225 = 23.75 = (23)75 = 875

3150 = 32.75 = (32)75=975

8 < 9 ⇒ 875 < 975

Vậy : 2225 < 3150

ta có: 2³³³ = (2³)¹¹¹ = 8¹¹¹

3²²² =(3²)¹¹¹ = 9¹¹¹

=> ....

TC \(2^{333}=\)\(2^{3.111}\)\(\left(2^3\right)^{111}=8^{111}\)

LC \(3^{222}=3^{2.111}=\left(3^2\right)^{111}=9^{111}\)

MÀ 8<9

\(\Rightarrow8^{111}< 9^{111}\)

\(hay\)\(2^{333}< 3^{222}\)

a: \(8+\dfrac{5}{13}\simeq8,\left(384615\right)< 8,415...\)

b: \(-\dfrac{4}{7}=-0.\left(571428\right)\)

\(1,\\ a,2^x=16=2^4\Rightarrow x=4\\ b,3^{x+1}=9^x=3^{2x}\\ \Rightarrow x+1=2x\Rightarrow x=1\\ c,2^{3x+2}=4^{x+5}=2^{2\left(x+5\right)}\\ \Rightarrow3x+2=2x+10\Rightarrow x=8\\ d,3^{2x-1}=243=3^5\\ \Rightarrow2x-1=5\Rightarrow x=3\\ 2,\\ a,2^{225}=8^{75}< 9^{75}=3^{150}\\ b,2^{91}=\left(2^{13}\right)^7=8192^7>3125^7=\left(5^5\right)^7=5^{35}\\ c,99^{20}=\left(99^2\right)^{10}< \left(99\cdot101\right)^{10}=9999^{10}\\ 3,\\ a,12^8\cdot9^{12}=2^{16}\cdot3^8\cdot3^{24}=2^{16}\cdot3^{32}=\left(2\cdot3^2\right)^{16}=18^{16}\\ b,75^{20}=\left(3\cdot5^2\right)^{20}=3^{20}\cdot5^{40}=\left(3^{20}\cdot5^{10}\right)\cdot5^{30}=\left(3^2\cdot5\right)^{10}\cdot5^{30}=45^{10}\cdot5^{30}\)

Bài 1:

a) \(\Rightarrow2^x=2^4\Rightarrow x=4\)

b) \(\Rightarrow3^{x+1}=3^{2x}\Rightarrow x+1=2x\Rightarrow x=1\)

c) \(\Rightarrow2^{3x+2}=2^{2x+10}\Rightarrow3x+2=2x+10\Rightarrow x=8\)

d) \(\Rightarrow3^{2x-1}=3^5\Rightarrow2x-1=5\Rightarrow x=3\)

Bài 2:

a) \(2^{225}=\left(2^3\right)^{75}=8^{75}< 9^{75}=\left(3^2\right)^{75}=3^{150}\)

b) \(2^{91}=\left(2^{13}\right)^7=8192^7>3125^7=\left(5^5\right)^7=5^{35}\)

c) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

Bài 3:

a) \(12^8.9^{12}=\left(4.3\right)^8.9^{12}=4^8.3^8.9^{12}=2^{16}.9^4.9^{12}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\)

b) \(75^{20}=\left(75^2\right)^{10}=5625^{10}=\left(45.125\right)^{10}=45^{10}.125^{10}=45^{10}.5^{30}\)

Ta có:3^34​>3³⁰=(3³)¹⁰=27¹⁰.

.         5²⁰=(5²)¹⁰=25¹⁰.

Vì 27>25=>27¹⁰>25¹⁰=>3³⁰>5²⁰.

Mà 3³⁴>3³⁰.

Nên 3³⁴>5²⁰.

3³⁴ = (3²)¹⁷

5²⁰ = (5²)¹⁰

Từ đó bạn làm tiếp

Cách 1:

Ta có: 9¹⁰ < 10¹⁰ < 10²⁰ => 9¹⁰ < 10²⁰

Cách 2: 

Ta có: 10²⁰ = (10²)¹⁰ = 100¹⁰ > 9¹⁰ => 10²⁰ > 9¹⁰

bài của tôi giống soyeon tiểu bài giảng ^^

               nhưng lãm cách 1 dễ hiểu hơn nhá

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ta có 64¹⁸ =(2⁶)¹⁸=2¹⁰⁸

16¹²=(2⁴)¹²=2⁴⁸

=>64¹⁸>16¹²

\(9^{70}=\left(9^7\right)^{10}=\left(\left(3^2\right)^7\right)^{10}=\left(3^{14}\right)^{10}\)

\(8^{100}=\left(2^3\right)^{100}=\left(\left(2^3\right)^{10}\right)^{10}=\left(2^{30}\right)^{10}\)

\(2^{30}>\left(2^4\right)^7>\left(3^2\right)^7=3^{14}\)

\(\Rightarrow2^{30}>3^{14}\Leftrightarrow9^{70}< 8^{100}\)

\(9^{70}=\left(9^7\right)^{10}=4782969^{10}\)

\(8^{100}=\left(8^{10}\right)^{10}=1073741824^{10}\)

\(4782969< 1073741824\)

\(\Rightarrow9^{70}< 8^{100}\)