Question

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

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

Answer 1

Answer: (B)

$f\left(x\right)=lo{g}_2\left(lo{g}_3\left(lo{g}_{4}x\right)\right)$ is defined if
$lo{g}_{3}lo{g}_4\left(x\right)>0$
$\Rightarrow lo{g}_4\left(x\right)>3^{\circ }=1$
$\Rightarrow lo{g}_4\left(x\right)>1$
$\Rightarrow x>4^1$
$\Rightarrow$ Domain is $\left(4,\infty \right)$