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1. If 3^(x+y) = 81 and 81^(x-y) = 3, then the value of x is = ?

A. 42

B. $\frac{15}{8}$

C. $\frac{17}{8}$

D. 39

Solution:

\begin{aligned} 3^{x + y} =  81 \\ 3^{x + y} = 3^{4} \\ x + y = 4..... (i) \\ 8 1^{x - y} = 3 \\ 3^{4 x - 4 y} = 3^{1} \\ 4 x - 4 y =  1 . . . . (ii) \\ From equation (i) and (ii) \\ 4 x - 4 y = 1 \\ 4 x + 4 y = 16 \\ 8 x = 17 \\ x = \frac{17}{8} \end{aligned}

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