The problme is, the "minimal" solution that you ask for is not the complete solution. You asked solve to provide a solution. How is solve to know that you want a half baked job, only a partial solution? Solve cannot read your mind.
Of course, if you knew in advance which parameters mattered to you, then you could manage things slightly better. So you might decide to choose in advance, that some of the parameters are perhaps zero. So you might decide to try setting all combinations of 4 of the 6 parameters to zero, and then seeing if solve can solve the problem in a way that makes you happy.
Or, you might look at the solution you did get, with essentially:
Sol.x2 = z5
Sol.u = pi + asin(log(z5)) + 2*pi*k
and then recognize that k has been introduced because there are infinitely many solutions. So set k==0, and then it reduces a bit. But now we still have the problem, is x2==z5 real? Is x2 bounded? is u real? Look at the original problem you posed. We see:
log(x2) + sin(u) == 0
But if x2 is such that log(x2) is greater than 1, or less than -1, then u will not be real valued. And of course, solve has not been told of any of that, so it cannot know how far to reduce the problem. But all of this is doing the thinking for solve, and if you do not want to do any thinking at all, then solve will be hopelessly stuck.
