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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
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot......\cdot\frac{31}{64}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{4\cdot6\cdot8\cdot....\cdot64}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot....\cdot31}{\left(2\cdot2\right)\cdot\left(3\cdot2\right)\cdot\left(4\cdot2\right)\cdot.....\cdot\left(2\cdot32\right)}=2^x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{\left(2\cdot2\cdot2\cdot....\cdot2\right)\left(1\cdot2\cdot3\cdot.....\cdot31\right)\cdot32}=2^x\)
\(\Leftrightarrow\frac{1}{2^{31}.2^5}=2^x\)
\(\Leftrightarrow\frac{1}{2^{36}}=2^x\)
\(\Rightarrow x=-36\)
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}...\frac{30}{62}.\frac{31}{64}\)
\(=\frac{1.2.3.4...30.31}{2.2.2.3.2.4.2.5...2.31.2.32}\)
\(=\frac{1.2.3.4...30.31}{2^{31}.\left(2.3.4.5...31\right).32}\)
\(=\frac{1}{2^{31}.32}\)
\(=\frac{1}{2^{31}.2^5}\)
\(=\frac{1}{2^{36}}\)
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}.....\frac{30}{62}.\frac{31}{64}=2^x\)
=>\(\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}....\frac{30}{2.31}.\frac{31}{2.32}=2^x\)
=>\(\frac{1.2.3.4.5....30.31}{2.2.2.3.2.4.2.5.2.6...2.31.2.32}=2^x\)
=>\(\frac{2.3.4.5...30.31}{2^{31}.32.\left(2.3.4.5...31\right)}=2^x\)
=>\(\frac{1}{2^{31}.2^5}=2^x\)
=>\(\frac{1}{2^{36}}=2^x\)
=> x=36
Vậy x=36
Chúc bn học tốt nhé!
\(\dfrac{1}{4}.\dfrac{2}{6}.\dfrac{3}{8}.\dfrac{4}{10}.\dfrac{5}{12}.....\dfrac{30}{62}.\dfrac{31}{64}=2^x\)
\(\Leftrightarrow\dfrac{1}{2.2}.\dfrac{2}{2.3}.\dfrac{3}{2.4}.\dfrac{4}{2.5}.\dfrac{5}{2.6}.....\dfrac{30}{2.31}.\dfrac{31}{2.32}=2^x\)
\(\Leftrightarrow\dfrac{1.2.3.4.5.....30.31}{2.2.2.3.2.4.2.5.2.6.....2.31.2.32}=2^x\)
\(\Leftrightarrow\dfrac{2.3.4.5.....30.31}{2^{31}.32.\left(2.3.4.5.....31\right)}=2^x\)
\(\Leftrightarrow\dfrac{1}{2^{31}.2^5}=2^x\)
\(\Leftrightarrow\dfrac{1}{2^{36}}=2^x\)
\(\Leftrightarrow2^{-36}=2^x\)
\(\Leftrightarrow x=-36\)
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}.....\frac{30}{62}.\frac{31}{64}\)
\(=\frac{1.2.3.4....30.31}{4.6.8.10.12....62.64}\)
\(=\frac{1.\left(2.3.4.5....30.31\right)}{2.\left(2.3.4....30.31\right).64}\)
\(=\frac{1}{2.64}\)
\(=\frac{1}{128}\)
\(\frac{1.2.3....31}{2^{30}.\left(2.3....31\right).32}=\frac{1}{2^{31}.32}=\frac{1}{2^{36}}=2^{-36}=2^x\)
Vậy x=-36
Hok tốt
\(\Rightarrow\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}...\frac{30}{2.31}.\frac{31}{2.32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}}.\frac{1.2.3.4....31}{2.3.4...32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}}.\frac{1}{32}=2^x\)
\(\Rightarrow\frac{1}{2^{31}.2^5}=2^x\)
\(\Rightarrow\frac{1}{2^{36}}=2^x\Rightarrow x=-36\)
