$if \log_{10} (x) - \log_{10} (y) = 1 and x + y = 11, then x =$

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Detailed Solution

$\log_{10} (x) - \log_{10} (y) = 1 \Rightarrow \log_{10} (\frac{x}{y}) = 1 \Rightarrow \frac{x}{y} = 1 \Rightarrow x = 10 y \Rightarrow x + y = 1 \Rightarrow 10 y + y = 11 \Rightarrow 11 y = 11 \Rightarrow y = 1 ∴ x = 10$

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