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![](https://rs.olm.vn/images/avt/0.png?1311)
b) \(3^{453}>3^{450}=\left(3^3\right)^{150}=27^{150}\)
\(5^{300}=\left(5^2\right)^{150}=25^{150}\)
\(27>25\Leftrightarrow27^{150}>25^{150}\)
nên \(3^{453}>5^{300}\).
a) \(2^{161}>2^{160}=\left(2^{16}\right)^{10}>13^{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có : \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)
\(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)
mà \(1000< 1024\)
\(\Rightarrow1000^{10}< 1024^{10}\)
\(\Rightarrow10^{30}< 2^{100}\)
b) Ta có : \(333^{444}=\left(111.3\right)^{444}=111^{444}.3^{444}=111^{444}.\left(3^4\right)^{111}=111^{444}.81^{111}\)
\(444^{333}=\left(111.4\right)^{333}=111^{333}.4^{333}=111^{333}.\left(4^3\right)^{111}=111^{333}.64^{111}\)
mà \(444>333\Rightarrow111^{444}>111^{333}\)
và \(81>64\Rightarrow81^{111}>64^{111}\)
\(\Rightarrow111^{444}.81^{111}>111^{333}.64^{111}\)
\(\Rightarrow333^{444}>444^{333}\)
c) Ta có : \(2^{161}>2^{160}=\left(2^4\right)^{40}=16^{40}>13^{40}\)
\(\Rightarrow2^{161}>13^{40}\)
d) Ta có : \(3^{453}>3^{450}=\left(3^3\right)^{150}=27^{150}>25^{150}=\left(5^2\right)^{150}=5^{300}\)
\(\Rightarrow3^{453}>5^{300}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
72^45-72^44=72^44(72-1)=72^44*71
72^44-72^43=72^43(72-1)=72^43*71
=>72^45-72^44>72^44-72^43
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/ \(13^{40}< 16^{40}=\left(2^4\right)^{40}=2^{160}< 2^{161}\)
2/ \(5^{300}=\left(5^2\right)^{150}=25^{150}\)
\(3^{453}=\left(3^3\right)^{151}=27^{151}\)
\(\Rightarrow25^{150}< 27^{150}< 27^{151}\Rightarrow5^{300}< 3^{453}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(5^{300}=\left(5^2\right)^{150}=25^{150}\)
\(3^{453}=(3^3)^{151}=27^{151}\)
Mà \(25^{150}< 27^{151}\Rightarrow5^{300}< 3^{453}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
5300 = (52)150 = 25150
3453 > 3450 = (33)150 = 27150
Vì 25150 < 27150 \(\Rightarrow\)5300 < 3453
5300 = (52)150 = 25150
3453 > 3450 = (33)150 = 27150
Vì 25150 < 27120
=> 5300 < 3453
Ủng hộ mk nha ^_-
cảm ơn soyeon_Tiểu bàng giải nhiều