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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