Michael Kleber writes:

<<
Mathematica vs Dan Asimov:

[I wrote:]

<<     PUZZLE:   Given that x^2 + log_10 (2x)  =  3, solve for x > 0 in closed form

[most of Mathematica session omitted here]

                    5 Log[10]
Out[2]= {{x -> Sqrt[---------]}}
                     Log[100]

Aah, much better.  I have no idea why it fails to recognize Log[10]/Log[100]. 
>>

OK, I'm impressed. It essentially solved it, though I agree it's mysterious why it screwed up with the last little simplification.  (Perhaps a repeated Simplify[], or a FullSimplify[], would do the trick?)

I wonder what kind of algorithm it used to solve such an offbeat equation.
(The answer, as you've all realized by now, is x = sqrt(10) / 2.)

--Dan