JEE MATHEMATICS MCQ: SET THEORY

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Which of the following is correct?

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Correct option: C

\frac{1}{\log _{\mathrm{xy}} \mathrm{xyz}}+\frac{1}{\log _{\mathrm{yz}} \mathrm{xyz}}+\frac{1}{\log _{\mathrm{zx}} \mathrm{xyz}}=2

Option C (

\frac{1}{\log _{\mathrm{xy}} \mathrm{xyz}}+\frac{1}{\log _{\mathrm{yz}} \mathrm{xyz}}+\frac{1}{\log _{\mathrm{zx}} \mathrm{xyz}}=2

) is correct because using the change of base formula and properties of logarithms, the expression simplifies to 2.

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