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If \(\log _3 x+\log _3 y=2+\log _3 2\) and \(\log _3(x+y)=2\), then
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Verified Answer
The correct answer is:
\(x=3, y=6\)
\(\begin{aligned}\text {Hints: }
& \log _3 \mathrm{x}+\log _3 \mathrm{y}=2+\log _3 2 \\
& \Rightarrow \mathrm{x} \cdot \mathrm{y}=18 \\
& \log (\mathrm{x}+\mathrm{y})=2 \Rightarrow \mathrm{x}+\mathrm{y}=9
\end{aligned}\)
we will get \(x=3\) and \(y=6\)
& \log _3 \mathrm{x}+\log _3 \mathrm{y}=2+\log _3 2 \\
& \Rightarrow \mathrm{x} \cdot \mathrm{y}=18 \\
& \log (\mathrm{x}+\mathrm{y})=2 \Rightarrow \mathrm{x}+\mathrm{y}=9
\end{aligned}\)
we will get \(x=3\) and \(y=6\)
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