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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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