Question

The domain of the function $f\left(x\right)={\log }_{10}{\log }_{10}{\log }_{10}{\log }_{10}x$ is

• A. $(0,\infty )$
• B. $(10,\infty )$
• C. $({10}^{10},\infty )$
• D. $({10}^{{10}^{10}},\infty )$

Answer 1

The correct option is C $({10}^{10},\infty )$

$f\left(x\right)={\log }_{10}{\log }_{10}{\log }_{10}{\log }_{10}x$
Domain,
${\log }_{10}{\log }_{10}{\log }_{10}x>0\Rightarrow {\log }_{10}{\log }_{10}x>1\Rightarrow {\log }_{10}x>10\Rightarrow x>{10}^{10}$