If $$\log \frac{a}{b} + \log \frac{b}{a} = $$   $$\,\log \left( {a + b} \right),$$   then -

A. a + b = 1

B. a - b = 1

C. a = b

D. a² - b² = 1

Answer: Option A

Solution(By Examveda Team)

$$\eqalign{ & \log \frac{a}{b} + \log \frac{b}{a} = \log \left( {a + b} \right) \cr & \Rightarrow \log \left( {a + b} \right) = \log \left( {\frac{a}{b} \times \frac{b}{a}} \right) \cr & \Rightarrow \log \left( {a + b} \right) = \log 1 \cr & So,\,\,\,a + b = 1 \cr} $$