\(\frac{18}{31}\)x\(\frac{62}{21}\)
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18/31 x 62/21 = 18x62/31x21 = 3x6x31x2/31x3x7=6x2/7=12/7
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{4}.\frac{2}{6}............\frac{31}{64}=2^x\)
\(\Rightarrow\frac{1.2........31}{2.2.2.3...........2.31.64}=2^x\)
\(\Rightarrow\frac{1}{2^{30}.2^4}=2^x\)
\(\Rightarrow\frac{1}{2^{34}}=2^x\)
\(\Rightarrow x=-34\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tính lần lượt 2 vế ta được:
-5 < x< -0,4
=> x = -4, -3, -2, -1, 0
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\(\Leftrightarrow-5< x< -\dfrac{1037}{1260}\)
=>\(x\in\left\{-4;-3;-2;-1\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot......\cdot\frac{31}{64}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{4\cdot6\cdot8\cdot....\cdot64}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{\left(2\cdot2\right)\cdot\left(3\cdot2\right)\cdot\left(4\cdot2\right)\cdot.....\cdot\left(2\cdot32\right)}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{\left(2\cdot2\cdot2\cdot....\cdot2\right)\left(1\cdot2\cdot3\cdot.....\cdot31\right)\cdot32}=2^x\)
\(\Leftrightarrow\frac{1}{2^{31}.2^5}=2^x\)
\(\Leftrightarrow\frac{1}{2^{36}}=2^x\)
\(\Rightarrow x=-36\)
\(\frac{18}{31}X\frac{62}{21}=\frac{18X62}{31X21}=\frac{6X2}{7}=\frac{12}{7}\)
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