Question

The domain of $f\left(x\right)={\log }_e|{\log }_{e}x|$ is.

• A. $(0,\infty )$
• B. $(1,\infty )$
• C. $(0,1)\cup (1,\infty )$
• D. $(-\infty ,1)$

Answer 1

Answer: (C)

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

$f\left(x\right)=log|logx|,\left(x\right)$ is defined if $|logx|>0$ and $x>0$

$i.e.,ifx>0$ and $x$ $\ne$ 1

$(\because |logx|>0ifx\ne 1)$

$\Rightarrow x\in (0,1)\cup (1,\infty )$.