\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}....\frac{15}{32}=\frac{1}{2}.\frac{1}{2}.\frac{1}{2}.\frac{2}{3}.\frac{1}{2}.\frac{3}{4}....\frac{1}{2}.\frac{15}{16}\)
\(=\left(\frac{1}{2}.\frac{1}{2}.....\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{15}{16}\right)\)
Số số \(\frac{1}{2}\)là (15-1):1+1=15 số
Do đó \(\left(\frac{1}{2}.\frac{1}{2}.....\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{15}{16}\right)=\left(\frac{1}{2}\right)^{15}.\frac{1.2.3....15}{2.3.4....15.16}\)
\(=\frac{1}{2^{15}}.\frac{1}{16}=\frac{1}{2^{15}}.\frac{1}{2^4}=\frac{1}{2^{15+4}}=\frac{1}{2^{19}}\)
\(\Rightarrow2^x=\frac{1}{2^{19}}\)
\(\Rightarrow x=-19\)
