\(\Leftrightarrow\dfrac{2\cdot3\cdot...\cdot31}{\left(2\cdot3\cdot...\cdot31\right)\cdot\left(2\cdot2\cdot...\cdot2\right)\cdot2^6}=2^x\)

=>2^x=1/2^36

=>x=-36

\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.....\dfrac{31}{64}\)

\(=\dfrac{2.3.....31}{\left(2.3.4.....31\right).\left(2.2.2.....2\right).2^6}\)(Ở phần 2 . 2 . 2 . ... . 2 có 30 số 2)

\(=\dfrac{1}{2^{30+6}}=\dfrac{1}{2^{36}}\)

\(\Rightarrow\dfrac{1}{2^{36}}=2^x\)

\(\Rightarrow2^{36}=2^{0-x}\)

\(\Rightarrow36=0-x\)

\(\Rightarrow x=-36\)

anh ơi 2 mũ 6 là mình lấy ở đâu ạ

ta co: 1/4=1/2(1+1) ;

2/6 = 1+1/2(2+1)..... 
=>ve trai =n/2(n+1).(n+1)/2(n+2).(n+2)/2(n+3)..... 
= (1/2)^36 
=> n= - 36

Trả lời 

\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.....\frac{30}{62}.\frac{31}{64}=2^x\)

\(\Leftrightarrow\frac{1}{2.2.2....2.64}=2^x\) ( 30 số hạng 2 ) 

\(\Leftrightarrow\frac{1}{2^{30}.2^6}=2^x\)

\(\Leftrightarrow\frac{1}{2^{36}}=2^x\)

\(\Rightarrow2^x=2^{-36}\)

\(\Rightarrow x=-36\)

Vậy \(x=-36\)

\(\frac{1}{4}\times\frac{2}{6}\times\frac{3}{8}\times...\times\frac{30}{62}\times\frac{31}{64}=2^x\)

\(\Rightarrow\) \(\frac{1\times2\times3\times...\times30\times31}{4\times6\times8\times...\times62\times64}=2^x\)

\(\Rightarrow\frac{1}{2^{31}}=2^x\)\(\Rightarrow1=2^x\times2^{31}\)

\(\Rightarrow2^{x+31}=2^0\)

\(\Rightarrow x+31=0\Rightarrow x=\left(-31\right)\)

Vân Anh thế còn \(\frac{1}{64}\)đâu