Q97 / 160 · WBJEE 2011 · Mathematics

If \(\log _3 x+\log _3 y=2+\log _3 2\) and \(\log _3(x+y)=2\), then

  • A
    \(x=1, y=8\)
  • B
    \(x=8, y=1\)
  • Correct answer
    C
    \(x=3, y=6\)
  • D
    \(x=9, y=3\)

Solution

\(\begin{aligned}\text {Hints: } & \log _3 \mathrm{x}+\log _3 \mathrm{y}=2+\log _3 2 \\ & \Rightarrow \mathrm{x} \cdot \mathrm{y}=18 \\ & \log (\mathrm{x}+\mathrm{y})=2 \Rightarrow \mathrm{x}+\mathrm{y}=9 \end{aligned}\) we will get \(x=3\) and \(y=6\)

Hence, the correct answer is option: 'C'.

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