• question_answer If ${{3}^{2x-\,y=}}{{3}^{\times +y=}}\,\,\sqrt{27}$, then the value of ${{3}^{x-y}}$ will be: A)  $\frac{1}{\sqrt{3}}$                 B)  $\frac{1}{\sqrt{27}}$ C)  $\sqrt{3}$                    D)  3

[c] ${{3}^{2x-\,y}}={{3}^{x+y}}=\sqrt{27}={{3}^{\frac{3}{2}}}$ $\Rightarrow \,\,\,2x-\,y=\frac{3}{2}\,\,x+y=\frac{3}{2}$ $4x-\,2y=3$ $2x+2y=3$ Solving equation (i) and (ii) $x=1$  $y=\frac{1}{2}$ $\Rightarrow \,\,\,{{3}^{1-\,\frac{1}{2}}}={{3}^{\frac{1}{2}}}=\sqrt{3}$