Question

The domain of $f\left(x\right)={\log }_5\left[{\log }_6\left[{\log }_{8}x\right]\right]$ is

• A. $x>4$
• B. $x>8$
• C. $x<8$
• D. $x<4$

Answer 1

The correct option is B

$x>8$

Explanation for the correct option(s)

Find the domain of $f\left(x\right)$

Consider the given function as,

$f\left(x\right)={\log }_5\left[{\log }_6\left[{\log }_{8}x\right]\right]$

For any logarithmic function ${\log }_a\left(b\right)$, $b>0$

$\Rightarrow {\log }_6\left[{\log }_{8}x\right]>0$

$$\begin{gathered} \Rightarrow {\log }_{8}x>6^0 \\ \Rightarrow x>8^1 \end{gathered}$$

Since, the domain of $f\left(x\right)$ is $x>8$

Hence, the correct answer is Option B.