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2^x nha

mình viết nhầm

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

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

=>\(\frac{1.2.3.4.5....30.31}{2.2.2.3.2.4.2.5.2.6...2.31.2.32}=2^x\)

=>\(\frac{2.3.4.5...30.31}{2^{31}.32.\left(2.3.4.5...31\right)}=2^x\)

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

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

=> x=36

Vậy x=36

Chúc bn học tốt nhé!

Ta có: \(\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}.......\frac{30}{2.31}.\frac{31}{64}=4^x\)

\(\frac{1}{2^{30}.64}=4^x\Leftrightarrow4^x.2^{30}.2^6=1\)

\(\Leftrightarrow2^{2x+36}2^0\)

\(\Leftrightarrow2x+36=0\)

\(\Leftrightarrow2x=-36\)

\(\Leftrightarrow x=-18\)

Vậy ........

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

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

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}.....\frac{30}{31}.\frac{31}{32}\right)=4^x\)

\(\Leftrightarrow\frac{1}{2}.\frac{1.2.3.4.5.....30.31}{2.3.4.5.6.....31.32}=4^x\)

\(\Leftrightarrow\frac{1}{2}.\frac{1}{32}=4^x\)

\(\Leftrightarrow4^x=\frac{1}{64}\)

\(\Leftrightarrow4^x.64=1\)

\(\Leftrightarrow4^x.4^3=1\Leftrightarrow4^{x+3}=4^0\Leftrightarrow x+3=0\Leftrightarrow x=-3\)

Vậy x = -3

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

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

\(\Leftrightarrow\frac{1.2.3.4.5...30.31}{2.2.2.3.2.4.2.5.2.6...2.31.2.32}=4^x\)

\(\Leftrightarrow\frac{2.3.4.5...30.31}{2^{31}.32.\left(2.3.4.5...31\right)}=4^x\)

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

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

\(\Leftrightarrow\frac{1}{4^{18}}=4^x\)

\(\Leftrightarrow x=-18\)

1/4.2/6.3/8.4/10.........30/62.31/64=4^x

^{=1/2.1/2.1/2.1/2.............1/2.1/64=4^x}

^{=1/2^30.1/2^6=4^x}

^{=1/2^36=4^x}

^{=1/4^18=4^x}

^=>x=-18

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

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**

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

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

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

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

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

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 :

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

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

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

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

\(\Leftrightarrow\dfrac{1.2.3.4.5.....30.31}{2.2.2.3.2.4.2.5.2.6.....2.31.2.32}=2^x\)

\(\Leftrightarrow\dfrac{2.3.4.5.....30.31}{2^{31}.32.\left(2.3.4.5.....31\right)}=2^x\)

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

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

\(\Leftrightarrow2^{-36}=2^x\)

\(\Leftrightarrow x=-36\)

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