The domain of the definition of the function f(x)=log4⁡log5⁡log3⁡18x−x2−77 is

Since log⁡x is defined for x>0 .  Therefore, for f(x)=log4⁡log5⁡log3⁡18x−x2−77log5⁡log3⁡18x−x2−77>0⇒log3⁡18x−x2−77>50⇒18x−x2−77>31⇒ x2−18x+80<0⇒ (x−8)(x−10)<0⇒ 8