Question

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

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

Answer 1

The correct option is B $(1,\infty )$

Consider $f\left(x\right)=lo{g}_e\left(A\right)$ where $A=lo{g}_{e}x$

Now for $f\left(x\right)$ to exist $A>0$ ...... $(\because logx$ exist for $x>0)$

$A>0\Rightarrow lo{g}_{e}x>0\Rightarrow x>1$

Domain of $f\left(x\right)$ is therefore $(1,\infty )$

Hence, option $\left(B\right)$ is correct.