If 2x=4y=8z and xyz=288, then 12x+14y+18z=

2x=22y=23z i.e., x=2y=3z=k (say).Then xyz=k36=288, So, K=12∴x=12, y=6, z=4. Therefore, 12x+14y+18z=1196

If 2x=4y=8z and xyz=288, then 12x+14y+18z=

2x=22y=23z i.e., x=2y=3z=k (say).Then xyz=k36=288, So, K=12∴x=12, y=6, z=4. Therefore, 12x+14y+18z=1196

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If $2^{x} = 4^{y} = 8^{z}$ and $xyz = 288,$ then $\frac{1}{2 x} + \frac{1}{4 y} + \frac{1}{8 z} =$

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$11 / 24$

$11 / 96$

$11 / 48$

$11 / 8$

answer is D.

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$2^{x} = 2^{2 y} = 2^{3 z} i . e ., x = 2 y = 3 z = k (say) .$

Then $xyz = \frac{k^{3}}{6} = 288, So, K = 12$

$∴ x = 12, y = 6, z = 4 .$ Therefore, $\frac{1}{2 x} + \frac{1}{4 y} + \frac{1}{8 z} = \frac{11}{96}$

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If $2^{x} = 4^{y} = 8^{z}$ and $xyz = 288,$ then $\frac{1}{2 x} + \frac{1}{4 y} + \frac{1}{8 z} =$