A) \[\frac{17}{8},\frac{9}{8}\]
B) \[\frac{17}{8},\frac{11}{8}\]
C) \[\frac{17}{8},\frac{15}{8}\]
D) \[\frac{11}{8},\frac{15}{8}\]
Correct Answer: C
Solution :
\[{{3}^{x+y}}=81\] \[\Rightarrow \] \[{{3}^{x+y}}={{3}^{4}}\] or \[x+y=4\] ? (i) Also \[{{(81)}^{x-y}}=3\] \[\Rightarrow \] \[{{3}^{4(x-y)}}={{3}^{1}},\,\,4x-4y=1\] ? (ii) Solving equations (i) and (ii), we get\[x=\frac{17}{8}\]and\[y=\frac{15}{8}\]
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