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JEE Main Mathematics question

MathematicsBasic Mathematics and LogarithmJEE Main

If are distinct positive numbers each being different from such that \left(\log_ba\cdot\log_ca-\log_aa\right)+\left(\log_ab\cdot\log_cb-\log_bb\right)+\left(\log_ac\cdot\log_bc-\log_cc\right)=0, then is

Answer: (C)

Solution

Put , , ; the condition becomes , i.e. . This factors as

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Question ID VK-013378