The domain of the real valued function f(x) = log e |log ex| is

$(0,1) \cup(1, \infty)$ $(0, \infty)$ $(e, \infty)$ $(1, \infty)$

$(0,1) \cup(1, \infty)$

For the domain |log x| > 0 ⇒ log x ≠ 0 ⇒ x > 0 ≠ 1 Hence (1) is the correct answer.