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

=>2^x=1/2^36

=>x=-36

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

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

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

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

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

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

\(\Rightarrow36=0-x\)

\(\Rightarrow x=-36\)

a)  (x-1)^x +2  = (x-1)^x +4

(x-1)^x - (x-1)^x = 4-2

0x = 2

=> \(x=\varphi\)

b) \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot\frac{5}{12}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=2^x\)

\(\frac{1\cdot2\cdot3\cdot4...\cdot30\cdot31}{2^{32}\left(1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31\right)\cdot32}=2^x\)

\(\frac{1}{64}=2^x\)

\(2^{-6}=2^x\)

\(x=-6\)