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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
\(\frac{1.2.3.4....30.31}{2.2.2.3.2.3.....2.32}=\frac{2.3.4....30.31}{2^{31}\left(2.3...31\right).32}=\frac{1}{2^{31}.2^5}=\frac{1}{2^{36}}=2^{-36}\)
Vậy x=-36
ta có \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}.....\frac{30}{62}\cdot\frac{31}{64}=2^x\)
=>\(\frac{1.2.3.4....31}{2\cdot2\cdot2\cdot3\cdot2\cdot3.....\cdot2\cdot3\cdot2}=\frac{2\cdot3\cdot4...30.31}{2^{31}\left(2\cdot3\cdot4...31\right)32}=\frac{1}{2^{31}\cdot2^5}=\frac{1}{2^{36}}=2^{-36}\)
\(=>x=-36\)
Ý A CẬU CHỈ CẦN
QUY ĐỒNG MẪU 18 VÀ 29 RỒI TÍNH
Ý B TƯƠNG TỰ
QUY ĐỒNG MẪU
CỦA 12 VÀ 31
a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)
\(=\frac{1x2x3x...x30x31}{2^{31}x\left(2x3x4x...x31x32\right)}=\frac{1}{2^{31}x32}=\frac{1}{2^{36}}\)
Có \(\frac{18}{18+19+20}>\frac{18}{18+19+20+21}\)
\(\frac{19}{18+19+21}>\frac{19}{18+19+20+21}\)
\(\frac{20}{18+19+21}>\frac{20}{18+19+20+21}\)
\(\frac{21}{18+19+21}>\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18}{18+19+20+21}+\frac{19}{18+19+20+21}+\frac{20}{18+19+20+21}+\frac{21}{18+19+20+21}\)
=> \(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>\frac{18+19+20+21}{18+19+20+21}\)
=>\(\frac{18}{18+19+20}+\frac{19}{18+19+21}+\frac{20}{18+19+21}+\frac{21}{18+19+21}>1\)
=>M>1
Còn lại mình không biết, đúng thì tick nha
b)
\(4\frac{5}{9}:2\frac{5}{18}-7< x< \left(3\frac{1}{5}:3,2+4,5.1\frac{31}{45}\right):\left(21.\frac{1}{2}\right)\)
\(\Rightarrow\frac{41}{9}:\frac{41}{18}-7< x< \left(\frac{16}{5}:\frac{16}{5}+\frac{9}{2}.\frac{76}{45}\right):\frac{21}{2}\)
\(\Rightarrow2-7< x< \left(1+\frac{38}{5}\right):\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{43}{5}:\frac{21}{2}\)
\(\Rightarrow-5< x< \frac{86}{105}\)
Vì \(x\in Z\left(gt\right)\)
\(\Rightarrow x\in\left\{-4;-3;-2;-1;0\right\}.\)
Vậy \(x\in\left\{-4;-3;-2;-1;0\right\}.\)
\(E=\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{4\cdot6\cdot8\cdot10\cdot...\cdot62\cdot64}=\frac{1\cdot1\cdot1\cdot1\cdot.....\cdot1\cdot1}{2\cdot2\cdot2\cdot....\cdot2\cdot64}=\frac{1}{2\cdot30\cdot64}=\frac{1}{3840}\)
18/31 x 62/21 = 18x62/31x21 = 3x6x31x2/31x3x7=6x2/7=12/7
\(\frac{18}{31}.\frac{62}{21}=\frac{18.62}{31.21}=\frac{3.6.31.2}{31.3.7}=\frac{6.2}{7}=\frac{12}{7}\)