Question

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

• A. $\left(1,+\infty \right)$
• B. $\left(0,+\infty \right)$
• C. $\left(e,+\infty \right)$
• D. None of these

Answer 1

Answer: (D)

None of these

Donain of $f\left(x\right)={\log }_e|{\log }_{e}x|$

for ${\log }_{e}x$ to be defined $x>0$

Also $|{\log }_{e}x|>0$

${\log }_{e}x\ne 0$

$x\ne 1$

$x\in (0,\infty )-\left\{1\right\}$

$D$ is correct