Question

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

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

Answer 1

The correct option is B

$\left(4,\infty \right)$

Explanation for correct answer Option(s)

Finding the domain of the function $f\left(x\right)$

The given function is defined as:

$$\begin{gathered} \Rightarrow {\log }_3\left({\log }_{4}x\right)>0 \\ \Rightarrow {\log }_{4}x>1 \end{gathered}$$

$$\begin{gathered} \Rightarrow x>4^1\left[\because \mathrm{if}{\log }_{a}x=b\mathrm{then}x=a^b\right] \\ \Rightarrow x>4 \end{gathered}$$

Hence, the domain of the given function is $\left(4,\infty \right)$

Therefore, Option B is correct.