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1. If 3^x+y = 81 and 81^x-y = 3, then the value of $\frac{x}{y}$ is = ?

A. $\frac{15}{17}$

B. $\frac{17}{30}$

C. $\frac{15}{34}$

D. $\frac{17}{15}$

Solution:

\begin{aligned} According to question, \\ \Rightarrow 3^{x + y} = 81 and 8 1^{x - y} = 3 \\ \Rightarrow 3^{x + y} = (3)^{4} and {(3)}^{4 (}^{x - y)} = 3^{1} \\ \Rightarrow x + y = 4 and x - y = \frac{1}{4} \\ x + y = 4...... (i) \\ x - y = \frac{1}{4} . . . . . (i i) \\ Solve the equation of (i) and (ii) \\ x = \frac{17}{8}, \\ y = \frac{15}{8}, \\ \Rightarrow \frac{x}{y} = \frac{17}{15} \end{aligned}

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