Comment #1 on issue 2040 by smichr: Better way to make a rational function out of an expression
http://code.google.com/p/sympy/issues/detail?id=2040

Sorry if this is too specific, but what about:

eq = sqrt(log(x**2 + 3*x + 2)*(log(x + 1) + log(x + 2)))
eq = eq.subs(dict((a,factor(a)) for a in eq.atoms(Add)))
eq = eq.subs(dict((a,logcombine(a, 1)) for a in eq.atoms(Add)))
from sympy.simplify.simplify import powdenest # issue 2039
powdenest(eq)
log((1 + x)*(2 + x))

{All the assumptions nonsense is bypassed with the logcombine 'assume_pos_real' argument. I think a nicer solution would be an easy way to change the assumptions on variables in one go--that was the intent of the discussion question I posed before looking at this.}

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