Domain of the function ${\log }_4{\log }_2{\log }_3\left(x^2+4x-23\right)$ is

The given function is defined when

${\log }_2{\log }_3\left(x^2+4x-23\right)>1$

i.e., when ${\log }_3\left(x^2+4x-23\right)>2$

i.e., when $x^2+4x-23>3^2$

i.e., when $x^2+4x-32>0$

i.e., when x < - 8 or x > 4