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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) $$\Large \frac{15}{4}$$

 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

$$\Large 2x = \frac{17}{4} = x = \frac{17}{8}$$

Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations

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