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

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

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

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

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

Vân Anh thế còn \(\frac{1}{64}\)đâu

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

\(\Rightarrow H=\frac{1.2.3...30.31}{2.2.2.3.2.4...2.31.2.32}=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}\)

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 \(x=-36\)

(1.2.3.4.5....31)/(2(1.2.3.4.5.....31).64)=2^x

1/(2.64)=2^x

1/128=2^x

2^-7=2^x

=>x=-7

cảm ơn bạn

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

=>2^x=1/2^36

=>x=-36