Prova 1

{x == Root[{ArcTan[1 - #1] + Log[#1] & , 3.0633197374531043503}]}

Plot[{ArcTan[1 - x] + Log[x], 0}, {x, -2., 3.}]

{x == Root[{ArcTan[1 - #1] + Log[#1] & , 3.0633197374531043503}]}