So sánh 2^101 và 5^39
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(2^{101}< 2^{100}\Leftrightarrow\left(2^5\right)^{20}=32^{20}\)
\(5^{39}< 5^{40}\Leftrightarrow\left(5^2\right)^{20}=25^{20}\)
Ta thấy: \(32^{20}>25^{20}\)
\(\Rightarrow2^{101}>5^{39}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
2^101 > 2^100 = (2^5)^20 = 32^20
5^39 < 5^40 = (5^2)^20 = 25^20
Do 32^20 > 25^20
=> 2^101 > 5^39
\(2^{101}< 2^{100}\Leftrightarrow\left(2^5\right)^{20}=32^{20}\)
\(5^{39}< 5^{40}\Leftrightarrow\left(5^2\right)^{20}=25^{20}\)
Do \(32^{20}>25^{20}\)
nên \(2^{101}>5^{39}\)
Vậy \(2^{101}>5^{39}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: 348 = (34)12 = 8112
436 = (43)12 = 6412
Vì 8112 > 6412 nên 348 > 436
Vậy 348 > 436.
Ta có: 2101 > 2100 => 2101 > (25)20 = 3220
539 < 540 => 539 < (52)20 = 2520
Vì 3220 > 2520 nên 2101 > 539
Vậy 2101 > 539.
a) \(3^{48}=3^{2.24}=\left(3^2\right)^{24}=9^{24}\)
\(4^{36}=\left(2^2\right)^{36}=2^{2.36}=2^{3.24}=\left(2^3\right)^{24}=8^{24}\)
Vì \(9>8\Rightarrow9^{24}>8^{24}\Rightarrow3^{48}>4^{36}\)
b) \(2^{101}>2^{91}=2^{7.13}=\left(2^7\right)^{13}=128^{13}\)
\(5^{39}=5^{3.13}=\left(5^3\right)^{13}=125^{13}\)
Vì \(128>125\Rightarrow128^{13}>125^{13}\Rightarrow2^{101}>128^{13}>5^{39}\)hay \(2^{101}>5^{39}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : 2101 > 2100 = ( 210)10 = 102410 > 62510 = ( 54)10 = 540 > 539
Vậy 2101 > 539
( Bài này sử dụng lũy thừa trung gian bạn nhé )
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
2^101 > 2^100 = (2^5)^20 = 32^20
5^39 < 5^40 = (5^2)^20 = 25^20
Do 32^20 > 25^20
=> 2^101 > 5^39