root[log(logx)-log(4-logx)-log3]=f(x) find domain

root[log(logx)-log(4-logx)-log3]=f(x)

 =>[log(logx)-log(4-logx)-log3] >_0

log(lox)-Log(4-logx)>_log3                 

                    using  loga-logb =log[a/b]  we get

 log[{logx} / {4- logx} ]>_log3                                   taking antilog both sides

[logx /{4-logx}] >_3

logx  >_ [12- 3 logx]

4logx>_12

logx>_3

x>_e cube

                                             x€ [e^3,infinity)