A) \[{{5}^{24}}\]
B) \[1\]
C) \[{{2}^{25}}\]
D) \[{{5}^{64}}\]
Correct Answer: D
Solution :
Given that, \[{{\log }_{2}}[{{\log }_{3}}\{{{\log }_{4}}({{\log }_{5}}x)\}]=0\] \[\Rightarrow \] \[{{\log }_{3}}\{{{\log }_{4}}({{\log }_{5}}x)\}={{2}^{0}}=1\] \[\Rightarrow \] \[{{\log }_{4}}({{\log }_{5}}x)={{3}^{1}}=a\] \[\Rightarrow \] \[{{\log }_{5}}\,\,x={{4}^{3}}=64\] \[\Rightarrow \] \[x={{5}^{64}}\]
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