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Let x , y , z > 1 and A = 1 log x y log x z log y x 2 log y z log z x log z y 3 . Then adj adj A 2 is equal to

Options

  1. A6 4
  2. B2 8
  3. C4 8
  4. D2 4

Correct answer

B. 2 8

Step-by-step solution

Given: A = 1 log x y log x z log y x 2 log y z log z x log z y 3 ⇒ A = 1 log y log x log z log x log x log y 2 log z log y log x log z log y log z 3 ⇒ A = 1 log x log y log z log x log y log z log x 2 log y log z log x log y 3 log z ⇒ A = 1 log x · log y · log z log x log y log z log x 2 log y log z log x log y 3 log z ⇒ A = log x · log y · log z log x · log y · log z 1 1 1 1 2 1 1 1 3 ⇒ A = 1 0 0 1 1 0 1 0 2 ⇒ A = 2 Now, adj adj A 2 = adj A 2 2 = A

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