Question
$${\text{If}}\,{\text{log}}\frac{a}{b} + {\text{log}}\frac{b}{a} = {\text{log}}(a + b),$$ then:
Answer: Option A
$$\eqalign{
& \log {a \over b} + \log {b \over a} = \log \left( {a + b} \right) \cr
& \Rightarrow \log \left( {a + b} \right) = \log \left( {{a \over b} \times {b \over a}} \right) = \log 1 \cr
& So,a + b = 1 \cr} $$
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$$\eqalign{
& \log {a \over b} + \log {b \over a} = \log \left( {a + b} \right) \cr
& \Rightarrow \log \left( {a + b} \right) = \log \left( {{a \over b} \times {b \over a}} \right) = \log 1 \cr
& So,a + b = 1 \cr} $$
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