What you probably forgot was the effect of having more than one planet.
For one planet, the research time should are more or less constant when you
have the same scaling of gain and cost.
However, when you colonize more planets, you get a prefactor
on the research gains, and break the equality..
If you want fast research without breaking the game, I would recommend a ratio of
at least 1.4 to 1.7. Still, this might break down for large games.
(Of course, for high tech levels, exponantial always wins over the prefactor,
but for tech levels < 30 this is not always the case).
For the more math-oriented:
cost=base_cost * cost_scale_factor^techlevel
output=output_per_lab * no_of_labs * output_scale_factor^techlevel (calculated as output per second)
This means that for the same scale factors, the output always wins (= the game breaks).
For close cases (almost equal scale factors) it depends on galaxy size and the number
of labs you build. However, as mentioned above, 1.4 and 1.7 should be reasonable
for fast research.