ket bn nha cau

mk dng ko co bn olm

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

\(\Leftrightarrow\)\(\frac{1.2.3.4.5.....30.31}{4.6.8.10.12.....62.64}=4^x\)

\(\Leftrightarrow\)\(\frac{2.3.4.5.....30.31}{2\left(2.3.4.5.....30.31\right).64}=4^x\)

\(\Leftrightarrow\)\(\frac{1}{128}=4^x\)

\(\Leftrightarrow\)\(2^{2x}=2^{-7}\) ( trong sgk có phần đọc thêm nói về cái này nhé ) 

\(\Leftrightarrow\)\(2x=-7\)

\(\Leftrightarrow\)\(x=\frac{-7}{2}\)

Vậy \(x=\frac{-7}{2}\)

Chúc bạn học tốt ~ 

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

\(=\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}....\frac{30}{2.31}.\frac{31}{2.32}=4^x\)

\(=\frac{1}{2^{31}.2^5}=4^x\)

\(=\frac{1}{2^{36}}=4^x\)

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

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

\(=-36=2.x\)

\(x.2=-36\)

\(x=-36:2\)

\(x=-18\)

1/4 . 2/6 . 3/8 . ... .30/62 .31/64 = 2^x

(1/2 . 1/2).(2/3 . 1/2).(3/4 . 1/2). ... .(30/31 . 1/2).(31/32 . 1/2) = 2^x

(1/2.1/2. ... .1/2).(1/2 . 2/3 . 3/4. ... .30/31 . 31/32) = 2^x

   (31 số 1/2) 

(1/2)^31.  = 2^x

=> 0=x+36

      x=0-36

      x=-36

Vậy x=-36

Theo mk nghĩ,mk làm đúng nha .Tk cho mk

Để mk sửa phần này một chút

\((\frac{1}{2})^{31}\cdot\frac{1\cdot2\cdot3.....30\cdot31}{2\cdot3\cdot4.....31\cdot32}=2^x\)

\(\frac{1^{31}}{2^{31}}\cdot\frac{1}{32}=2^x\)

\(\frac{1}{2^{31}}\cdot\frac{1}{2^5}=2^x\)

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

\(1=2^x\cdot2^{36}\)

\(2^0=2^x+36\)

Rồi bn tự suy luận nha

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

Có 31 thừa số

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}\right)...................\left(\frac{1}{2}.\frac{31}{32}\right)=\frac{1}{2^x}\)

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}...............\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}...............\frac{31}{32}\right)=\frac{1}{2^x}\)

Có 31 thừa số                                            Có 31 thừa số

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1.2....................31}{2.3..............32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{2^5}=\frac{1}{2^x}\)

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

\(\Leftrightarrow x=36\)

Vậy x=36

Chúc bạn học tốt

\(\frac{1.2.3....31}{2^{30}.\left(2.3....31\right).32}=\frac{1}{2^{31}.32}=\frac{1}{2^{36}}=2^{-36}=2^x\)

Vậy x=-36

Hok tốt

\(\frac{1.2.3.4....30.31}{2.2.2.3.2.3.....2.32}=\frac{2.3.4....30.31}{2^{31}\left(2.3...31\right).32}=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}=2^{-36}\)

Vậy x=-36

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

=>\(\frac{1.2.3.4....31}{2\cdot2\cdot2\cdot3\cdot2\cdot3.....\cdot2\cdot3\cdot2}=\frac{2\cdot3\cdot4...30.31}{2^{31}\left(2\cdot3\cdot4...31\right)32}=\frac{1}{2^{31}\cdot2^5}=\frac{1}{2^{36}}=2^{-36}\)

\(=>x=-36\)

trong cái xã hội này có làm thì mới có ăn,ko lam mà ăn chỉ có ăn đầu b** ăn c**

\(\Rightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=2^x\)

\(\Rightarrow\frac{1}{2^{31}}.\frac{1.2.3.4....31}{2.3.4...32}=2^x\)

\(\Rightarrow\frac{1}{2^{31}}.\frac{1}{32}=2^x\)

\(\Rightarrow\frac{1}{2^{31}.2^5}=2^x\)

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

xin lỗi mik mới lớp 6

-4;-3;-2;-1 nha bạn.

\(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5\cdot1\frac{31}{45}\right):\left(-21\frac{1}{2}\right)\)

\(\Leftrightarrow\frac{41}{9}:\frac{41}{18}-7< x< \left(\frac{16}{5}:\frac{16}{5}+\frac{9}{2}\cdot\frac{76}{45}\right):\left(-\frac{43}{2}\right)\)

\(\Leftrightarrow\frac{41}{9}\cdot\frac{18}{41}-7< x< \frac{43}{5}:\left(-\frac{43}{2}\right)\)

\(\Leftrightarrow2-7< x< -\frac{2}{5}\)

\(\Leftrightarrow-5< x< -0,4\)

\(\Leftrightarrow x\in\left\{-4;-3;-2;-1\right\}\)

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

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot.....\cdot\frac{30}{31}\cdot\frac{31}{32}\right)=2^x\)

\(\Leftrightarrow\frac{1}{32}=2^{x+1}\)

Làm nốt.

ko làm được câu này hay câu b ib với tớ nha.khẳng định tối giải.

Câu b thôi các bạn nhé, câu a mình ko cần nx với cả mình ghi sai dữ liệu câu a r

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

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{4\cdot6\cdot8\cdot10\cdot...\cdot62\cdot64}=2x\)

\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot5\cdot2\cdot....\cdot31\cdot2\cdot32\cdot2}=2x\)

\(\Leftrightarrow\frac{1}{2\cdot2\cdot2\cdot2\cdot....\cdot2\cdot2\cdot32}=2x\)

Có  : (31 - 1) : 1 + 1 = 31 (thừa số 2) 

\(\Rightarrow\frac{1}{2^{31}.32}=2x\)

\(\Rightarrow x=\frac{1}{2^{31}.32}\div2\)

b, \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)

\(\Leftrightarrow x+1=x+4\)

\(\Leftrightarrow0=3\text{ (vô lý) }\)

Tìm x biết :             \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}...\frac{30}{62}.\frac{31}{64}=2x\) 

 Biến đổi mẫu thức của vế trái :     \(\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=2x\)   Giản ước vế trái đực :

                                               \(\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{1}{2}...\frac{1}{2}.\frac{1}{2.32}=2x\)        (*)   

                                                  \(\Leftrightarrow\frac{1}{2^{36}}=2x\Leftrightarrow x=\frac{1}{2^{37}}\)