• If \( \Large 3^{x+y}=81 \) and \( \Large 81^{x-y}=3 \), then what is the value of x?

    A) \( \Large \frac{17}{16} \)

      B) \( \Large \frac{17}{8} \)

    C) \( \Large \frac{17}{4} \)

      D) \( \Large \frac{15}{4} \)

    Correct Answer:
      B) \( \Large \frac{17}{8} \)

    Description for Correct answer

    Given,

    \( \Large 3^{x+y}=51 \)

    = \( \Large 3^{x+y}=3^{4} \)

    = x + y = 4 ...(i)

    and \( \Large 81^{x-y}=3 \  or \  \left(3^{4}\right)^{x-y}=3^{1} \)

    = \( \Large x-y = \frac{1}{4} \) ...(ii)

    On solving the Eqs. (i) and (ii), we get

    \( \Large 2x = \frac{17}{4} = x = \frac{17}{8} \)


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