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For positive numbers x, y and z, evaluate the determinant of the matrix with rows [1, logₓ y, logₓ z], [log_y x, 1, log_y z], [log_z x, log_z y, 1].

1. 0
2. log(xyz)
3. log(x + y + z)
4. (log x)(log y)(log z)

Correct answer: 0

Solution

Converting to a common base, each row becomes proportional to (log x, log y, log z), so two rows are linearly dependent and the determinant is 0.

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