so sánh 9 mux12 và 27 mũ 7
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So Sánh
12 mũ 18 và 5 mũ 27
12 mũ 18 và 27 mũ 6.169
4 mũ 4 và 64 mũ 7
2009 mũ 10+2009 mũ 9 và 2010 mũ 10
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)2437=(35)7=335 ; 910.275=330.315=345.
Vì 35 < 45 => 335<345=>2437<910.275.
b) 1511=311.511;813.1255=312.515.
Vì 311<312 và 511<515 => 311.511<312.515 => 1511 < 813.1255
![](https://rs.olm.vn/images/avt/0.png?1311)
Mời thí chủ nhận bài:)), sai nhớ bảo tôi thí chủ đừng giấu:))
Ta có: 930= (32)30 = 360
2720= (33)20 = 360
⇒⇒ 930 = 2720
so sánh 2210 và 5140
Ta có: 2210= (23)70 = 870
5140 = (52)70=2570
Mà : 870 < 2570
⇒⇒ 2210<5140
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Có: \(^{9^{36}}\)=\(^{\left(3^2\right)^{36}}\)=\(3^{72}\)
\(27^{10}\)=\(\left(3^3\right)^{10}\)=\(3^{30}\)
Vì 3 mũ 72 > 3 mũ 30 suy ra 9 mũ 36 > 27 mũ 10
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\dfrac{1}{27}\right)^{10}=\dfrac{1}{27^{10}}=\dfrac{1}{\left(3^3\right)^{10}}=\dfrac{1}{3^{30}}\)
\(\left(\dfrac{1}{81}\right)^7=\dfrac{1}{81^7}=\dfrac{1}{\left(3^4\right)^7}=\dfrac{1}{3^{28}}\)
Do \(3^{30}>3^{28}\Leftrightarrow\dfrac{1}{3^{30}}< \dfrac{1}{3^{28}}\)
\(\Leftrightarrow\left(\dfrac{1}{27}\right)^{10}< \left(\dfrac{1}{81}\right)^7\)
Ta có:
\(\left(\dfrac{1}{27}\right)^{10}=\left(\dfrac{1}{3^3}\right)^{10}=\left(\dfrac{1}{3}\right)^{30}\)
\(\left(\dfrac{1}{81}\right)^7=\left(\dfrac{1}{3^5}\right)^7=\left(\dfrac{1}{3}\right)^{35}\)
Vì \(\left(\dfrac{1}{3}\right)^{35}>\left(\dfrac{1}{3}\right)^{30}\)
⇒\(\left(\dfrac{1}{27}\right)^{10}< \left(\dfrac{1}{81}\right)^7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có :
\(27^{27}>27^{26}=\left(27^2\right)^{13}=729^{13}>243^{13}\)
\(\Rightarrow27^{27}>243^{13}\)
\(\Rightarrow-27^{27}< -243^{13}\)
\(\Rightarrow\left(-27\right)^{27}< \left(-243\right)^{13}\)
b) \(\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{8}\right)^{26}=\left(\dfrac{1}{8^2}\right)^{13}=\left(\dfrac{1}{64}\right)^{13}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(\dfrac{1}{8}\right)^{25}>\left(\dfrac{1}{128}\right)^{13}\)
\(\Rightarrow\left(-\dfrac{1}{8}\right)^{25}< \left(-\dfrac{1}{128}\right)^{13}\)
c) \(4^{50}=\left(4^5\right)^{10}=1024^{10}\)
\(8^{30}=\left(8^3\right)^{10}=512^{10}< 1024^{10}\)
\(\Rightarrow4^{50}>8^{30}\)
d) \(\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{9}\right)^{12}< \left(\dfrac{1}{27}\right)^{12}\)
\(\Rightarrow\left(\dfrac{1}{9}\right)^{17}< \left(\dfrac{1}{27}\right)^{12}\)
277= (93)7=921 > 912
\(9^{12}\)\(=\left(3^2\right)^{12}\)\(=3^{2x12}\)\(=3^{24}\)
\(27^7\)\(=\left(3^3\right)^7\)\(=3^{3x7}\)\(=3^{21}\)
\(3^{24}\)\(>3^{21}\)\(=>9^{12}\)\(>27^7\)