A) \[5\sqrt{5}\]
B) \[\sqrt{5}\]
C) \[25\sqrt{5}\]
D) \[125\]
Correct Answer: C
Solution :
\[{{4}^{x}}-{{4}^{x-1}}=24\Rightarrow {{4}^{x}}-\frac{{{4}^{x}}}{4}=24\] \[\Rightarrow \]\[{{4}^{x}}=8\times 4\Rightarrow {{2}^{2x}}={{2}^{5}}\Rightarrow x=\frac{5}{2}\] \[\therefore \]\[{{(2x)}^{2}}={{\left( 2x\frac{5}{2} \right)}^{{\scriptstyle{}^{5}/{}_{2}}}}={{5}^{{}^{5}/{}_{2}}}={{5}^{2}}\,{{5}^{{}^{1}/{}_{2}}}\] \[25\sqrt{5}\]
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