A) \( \Large \frac{17}{16} \) |
B) \( \Large \frac{17}{8} \) |
C) \( \Large \frac{17}{4} \) |
D) \( \Large \frac{15}{4} \) |
B) \( \Large \frac{17}{8} \) |
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
\( \Large 2x = \frac{17}{4} = x = \frac{17}{8} \)