Assuming that "log" is the common logarithm (base 10) and that the angle is in radians, x=1.160501. I cheated, though, and used a graphing calculator once I got it down to -12xlog(x+1/4)=tan(x+4). Summer has blitzed my mind and I've forgotten the necessary calculus to solve this completely by hand. (I'm pretty sure calculus can solve it, at least.)
Totally the entire left side is solvable by any freshman with half a brain. the tangent and Log is a different matter, but this can be solved entirely by hand.
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