Question

Domain of $f\left(x\right)=\log |\log x|$ is

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

Answer 1

The correct option is C $(0,1)\cup (1,\infty )$

Given:$f\left(x\right)=\log \left|\log x\right|$

$\Rightarrow \left|\log x\right|>0$ and $x>0$

$\Rightarrow x\in R$

$\Rightarrow x\in (0,\infty )$ since $x>0$

Again $\left|\log x\right|\ne 0$

$\Rightarrow x\ne 1$

$\therefore x\in (1,\infty )$

Hence domain is $x\in (0,1)\cup (0,\infty )$