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If \(\\log \frac{x}{y} + \log \frac{y}{x} = \log (x + y)\), then :1. x + y = 12. x - y = 13. x2 - y2 = 14. x = y |
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Answer» Correct Answer - Option 1 : x + y = 1 CONCEPT: Product property of logarithms is given by \(\log a + \log b = \log (a \times b)\) CALCULATION: Given that \(\\log \frac{x}{y} + \log \frac{y}{x} = \log (x + y)\) \(\begin{gathered} \log \frac{x}{y} + \log \frac{y}{x} = \log (x + y) \hfill \\ ⇒ \log (x + y) = \log (\frac{x}{y} \times \frac{y}{x}) \hfill \\ \end{gathered} \) ⇒ log (x + y) = log (1) ∴ x + y = 1 Therefore option (1) is the correct answer. |
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