When you log transform data what is being tested on the original scale
of the data?
When you log transform data, you change additive relationships to multiplicative ones. If you take log(x) you change:
If x goes up from 1 to 2, or 2 to 3, or 10 to 11 etc. what happens to y?
If x goes from 1 to 2, or 2 to 4, or 10 to 20, or 20 to 40 etc. what happens to y?
And why can we use our log transformed data to answer our scientific
It's not at all clear that you can do this. It depends on what your question is. If it is very vague (if x goes up, does y go up?) then perhaps you can. If it is a multiplicative question (if x doubles, what happens to y?) then taking the log makes it possible to answer your question. But sometimes taking logs makes it harder or impossible to answer your question.
This is a reason why I often say that you should take logs (or other transformations) for substantive reasons, not statistical ones.
You took log of time. It's not completely clear to me exactly analysis you did - it looks like a t-test but maybe survival analysis - but if you did a t-test then you changed the scale of "survival time". So, how do you want to look at survival time? On the original scale, 1 year, 2 years, 3 years, 4 years are equidistant from each other. On the log scale they are not. On the log scale, 1 year, 2 years, 4 years, 8 years are equidistant.
Are you after "survived 3 years longer" or "survived 1.3 times as long"?