यदि `2^(x) = 3^(y) = 12^(z)` हो , तब `(x +2y)//(xy)` किसके बराबर है ?

Options

A. z
B. 1/z
C. 2z
D. z/2

Answer

B

Explanation

माना ` 2^(x) = 3^(y) = 12^(z) = k`
` rArr x = log_(2) k, y = log_(3) k, z = log_(12) k`
अब , ` (x + 2y)/(xy) = (log_(2) k+2 log_(3) k)/(log_(2) k*log_(3) k) = 1/(log_(3) k) + 2/(log_(2) k) `
` = log_(k) 3 + 2 log_(k) 2 = log_(k) 3 + log_(k) 4 = log_(k) 12 `
` = 1/(log_(12) k) = 1/z`