\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}.....\frac{30}{62}.\frac{31}{64}=4^x\)
\(\Leftrightarrow\)\(\frac{1.2.3.4.5.....30.31}{4.6.8.10.12.....62.64}=4^x\)
\(\Leftrightarrow\)\(\frac{2.3.4.5.....30.31}{2\left(2.3.4.5.....30.31\right).64}=4^x\)
\(\Leftrightarrow\)\(\frac{1}{128}=4^x\)
\(\Leftrightarrow\)\(2^{2x}=2^{-7}\) ( 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 ~
\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}.....\frac{30}{62}.\frac{31}{64}=4^x\)
\(=\frac{1}{2.2}.\frac{2}{2.3}.\frac{3}{2.4}.\frac{4}{2.5}.\frac{5}{2.6}....\frac{30}{2.31}.\frac{31}{2.32}=4^x\)
\(=\frac{1}{2^{31}.2^5}=4^x\)
\(=\frac{1}{2^{36}}=4^x\)
\(=\frac{1}{2^{36}}=2^{2x}\)
\(=2^{-36}=2^{2x}\)
\(=-36=2.x\)
\(x.2=-36\)
\(x=-36:2\)
\(x=-18\)
