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