Question

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

• A. $[4,\infty )$
• B. $(4,\infty )$
• C. $-\infty ,4)$
• D. None of these

Answer 1

The correct option is B $(4,\infty )$

$f\left(x\right)$ is defined if ${\log }_3{\log }_{4}x>0,{\log }_{4}x>0$ and $x>0$

$\Rightarrow {\log }_{4}x>3^0=1,x>4^0$ and $x>0$

$\Rightarrow x>4^1,x>1$ and $x>0\Rightarrow x>4$

Domain of $f\left(x\right)=(4,\infty )$

Hence option (B) is correct