A) \[(-\infty ,4)\]
B) \[(4,\infty )\]
C) \[(0,4)\]
D) \[(1,\infty )\]
E) \[(-\infty ,1)\]
Correct Answer: B
Solution :
Given, \[f(x)={{\log }_{2}}({{\log }_{3}}({{\log }_{4}}x))\] We know\[{{\log }_{a}}x\]is positive, if\[x>a\] and\[{{\log }_{a}}x\]is negative, if \[x<a\] For\[f(x)\]to be defined \[{{\log }_{3}}{{\log }_{4}}x>0,{{\log }_{4}}x>0\]and \[x>0\] \[\Rightarrow \] \[{{\log }_{4}}x>{{3}^{0}}=1,x>{{4}^{0}}\]and \[x>0\] \[\Rightarrow \] \[x>4,x>1\]and \[x>0\] \[\Rightarrow \] \[x>4\]
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