XAT 2021 Question 1

Question 1

If $$\log_4m + \log_4n = \log_2(m + n)$$ where m and n are positive real numbers, then which of the following must be true?

Solution

$$\log_4mn=\log_2(m+n)$$ 

$$\sqrt{\ mn}=(m+n)$$

Squarring on both sides

$$m^2+n^2+mn\ =\ 0$$

Since m, n are positive real numbers, no value of m and n satisfy the above equations.


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