Explanation

(d)
Given, $\log_{2}{\left\lbrack \log_{3}\left\{ \log_{4}\left( \log_{5}x \right) \right\} \right\rbrack = 0}$
$\Rightarrow \log_{3}{\left\{ \log_{4}\left( \log_{5}x \right) \right\} = 2^{0} = 1}$
$\Rightarrow \log_{4}{\left( \log_{5}x \right) = 3}$
$\Rightarrow \log_{5}{x = 4^{3} = 64}$
$\Rightarrow x = 5^{64}$