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Comment #7 on issue 2043 by asmeurer: log should not expand(1/x) (was "expand log can be more complete" and "logcombine can be less strict")
http://code.google.com/p/sympy/issues/detail?id=2043

Making all symbols positive is not sufficient to do all operations. If x and y are positive, x - y could still be negative, meaning you still can't do anything with log((x - y)*(x + y)) if you want to be rigorous.

Instead of forcing assumptions on the arguments of the log itself, I think it should instead be possible to assume that log itself is a real-valued function. It could be with the new assumptions with something like Assume(log, Q.real), or maybe a kwarg to log (log(x, real=True)), though the easiest way is to just make all important functions that do log manipulation have symbolic kwargs.

On the other hand, I really do thing as I mentioned before somewhere that it could be useful to have some kind of "meta-assumption" in the new assumptions, along the lines of Assume(expr, Q.nice_things) (maybe Q.symbolic) that does what your posify is purporting to do.

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