Question

1/4×2/6×3/8×4/10×5/12••••••••31/64=1/2^x

Answer 1

$\frac{1}{4} \times \frac{2}{6} \times \frac{3}{8} \times \frac{4}{10} \times \frac{5}{12}\cdot \cdot\cdot\frac{31}{64} = \frac{1}{2^{x}}$

$\implies \frac{1}{2\times 2} \times \frac{2}{2\times 3} \times \frac{3}{2\times 4} \times \frac{4}{2\times 5} \times \frac{5}{2\times 6}\cdot \cdot\cdot\frac{30}{2\times 31}\times \frac{31}{64} = \frac{1}{2^{x}}$

$\implies \frac{1}{2} \times \frac{1}{2} \times \cdot \cdot \cdot 30 \: times \times \frac{1}{64} = \frac{1}{2^{x}}$

$\implies \frac{1}{2^{30}} \times \frac{1}{2^{6}} = \frac{1}{2^{x}}$

$\implies \frac{1}{2^{30+6}} = \frac{1}{2^{x}}$

$\implies \frac{1}{2^{36}} = \frac{1}{2^{x}}$

$\implies \Big(\frac{1}{2}\Big)^{36} = \Big(\frac{1}{2} \Big)^{x}$

$\implies x = 36$

$\boxed { \pink { If \: a^{m} = a^{n} \implies m = n }}$

Therefore.,

$\red { Value \:of\: x } \green {= 36}$

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