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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
So sánh:\(10^{10}\) và \(48.50^5\)
Ta có:
\(10^{10}=10^{2.5}=\left(10^2\right)^5=100^5=\left(2.50\right)^5=2^5.50^5=32.50^5\)
Vì \(32.50^5< 48.50^5\)
\(\Rightarrow10^{10}< 48.50^5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(7^{50}=\left(7^5\right)^{10}=16807^{10}>2197^{10}=\left(13^3\right)^{10}=13^{30}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
2021/2023=1-2/2023
101/103=1-2/103
mà 2/2023<2/103
nên 2021/2023>101/103
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có:
\(5^4=625\)
\(4^5=1024\)
vì \(625< 1024\)nên
\(\Rightarrow5^4< 4^5\)
\(\frac{5}{4}\)>1
\(\frac{4}{5}\)<1
suy ra \(\frac{4}{5}\)<1\(\frac{5}{4}\)
vay \(\frac{4}{5}\)<\(\frac{5}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
2014/2015=20142014/20152015
Vì 20142014<20142015 nên 20142014/20152015<20142015/20152015
=> Nó <
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có :
\(\hept{\begin{cases}12^{44}=\left(12^4\right)^{11}=\left(2^8.3^4\right)^{11}\\9^{66}=\left(9^6\right)^{11}=\left(3^{12}\right)^{11}\end{cases}}\)
mà ta có \(2^8.3^4< 3^8.3^4=3^{12}\text{ nên }\left(2^8.3^4\right)^{11}< \left(3^{12}\right)^{11}\)
hay ta có \(12^{44}< 9^{66}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
10750=(1072)25=1144925
7375=(733)25=38901725
vì 11449<389017 nên 1144925<38901725
hay 10750<7375