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  4. If E=(1/4) ⋅ (2/6) ⋅ (3/8) ⋅ (4/10) ⋅s (30/62) ⋅ (31/64)=8x, then value of x is

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Q. 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

Permutations and Combinations

Solution:

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