Question

If $E=\frac{1}{4}\cdot \frac{2}{6}\cdot \frac{3}{8}\cdot \frac{4}{10}\cdots \frac{30}{62}\cdot \frac{31}{64}=8^x$, then value of $x$ is

• A. -7
• B. -9
• C. -10
• D. -12

Answer 1

Answer: (D)

$E=\frac{31!}{2^{31}(32!)}=\frac{1}{2^{31}(32)}=\frac{1}{2^{36}}=2^{-36}={\left(2^3\right)}^{-12}=8^{-12}$
Thus, $x=-12$.