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  4. The domain of the function f(x)=log2(log3(log4 x)) is

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Q. The domain of the function $f\left(x\right)=log_{2}\left(log_{3}\left(log_{4}\,x\right)\right)$ is

Relations and Functions

Solution:

$f\left(x\right)=log_{2}\left(log_{3}\left(log_{4}\,x\right)\right)$ is defined if
$log_{3}\,log_{4}\left(x\right) > 0$
$\Rightarrow log_{4}\left(x\right) > 3^{\circ}=1$
$\Rightarrow log_{4}\left(x\right) > 1$
$\Rightarrow x > 4^{1}$
$\Rightarrow $ Domain is $\left(4, \infty\right)$