If x >= y and y > 1, then the value of the expression log_x (x/y) + log_y (y/x) can never be

CAT 2005 Question Paper Question 18

Question 18

If x >= y and y > 1, then the value of the expression $$log_x (x/y) + log_y (y/x)$$ can never be

Solution

$$log_x (x/y) + log_y (y/x)$$ = $$1 - log_x (y) + 1 - log_y (x)$$
= $$2 - (log_x y + 1/log_x y)$$ <= 0 (Since $$log_x y + 1/log_x y$$ >= 2)
So, the value of the expression cannot be 1.

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