Mathcad (resp. muPad) defaults to working in the complex plane where e.g. the logarithm is not unique and the rules we are used from the reals space do not apply in the same way.
So I guess we don't see a bug here.
If we tell Mathcad/muPad that we would like to stay in reals space (meaning the log arguments are all positive reals) does the trick
I guess what we see in your example is not a bug but rather the result of a very cautious behavior of a mediocre symbolic engine. MuPad is not aware in the first step that the equation ln(9-y)-ln(y)=ln(2) has no other (not even non-real) solutions but y=3.
If we ask Mupad for the solutions of this equation explicitly it seems to realize that 3 is the only solution.
Alas, we know that muPad is not the symbolic engine we would like to see to work under the hood of Mathcad. And i see no plans that PTC would like to change over to a better symbolics, rather the change is that Mathcad itself is losing quality in a catastrophic way, so the mediocre Symbolic may be the considered best part of it.
