Question

The domain of the function $f\left(x\right)={\log }_2\left({\log }_3\left({\log }_{4}x\right)\right)$ is

• A. $(-\infty ,4)$
• B. $(4,-\infty )$
• C. $(0,4)$
• D. $(1,-\infty )$

Answer 1

Answer: (A)

$(-\infty ,4)$

$f\left(x\right)={\log }_2\left({\log }_3\right({\log }_{4}x\left)\right)$

$\Rightarrow {\log }_3\left({\log }_{4}x\right)>0$

$\Rightarrow {\log }_{4}x>3^0$

$\Rightarrow {\log }_{4}x>1$

$\Rightarrow x>4^1$

$\Rightarrow x>4$