log₁₀log₂log_2/pi(tan^-1x)^-1

Every base in above expression is +ve & not equal to 1 so that part of the requirement is fulfilled.

For tan^-1x to be defined x could take any real value.

For (tan^-1x)^-1 to be defined x could take any real value except where tan^-1x=0 ;i.e. x ≠0.

For log_2/pi(tan^-1x)^-1 to be defined (tan^-1x)^-1 >0 ;i.e. x>0.

For log₂log_2/pi(tan^-1x)^-1  to be defined  log_2/pi(tan^-1x)^-1 >0;or,(tan^-1x)^-1 >1;or, tan^-1x<1;or,x<tan(1 radian).

At last for log₁₀log₂log_2/pi(tan^-1x)^-1 to be defined log₂log_2/pi(tan^-1x)^-1 >0;or, log_2/pi(tan^-1x)^-1 >1

or, (tan^-1x)^-1 <2/pi                 ....[coz' (2/pi)<1]

or, tan^-1x>pi/2 which couldn't be possible for any real x.    ---[-¶/2≤tan^-1x≤¶/2;principal values.]

Hence the given expression is not defined for any x or it's domain is a null set.

This could be easily deducted by doing last step first & such kind of intution could be mastered by good practice.I just give these steps for the thoroughness.