Use the level or logarithm of GDP in HP filter?

[cuccu]

I see that in research papers their authors usually apply the HP filter with ln(GDP) instead of GDP at level, in order to find out business cycles.
Actually thus far I have not understood mathematical implications regarding using the logarithm (How to link to a recession?...). Any explanation in detail is much appreciated.

[startz]

GDP has roughly constant percentage growth over long periods, as opposed to linear growth. Hence the log transformation.

[cuccu]

Hi startz, what advantage would we have when applying the HP filter to this transformed series?
(You could show me in form of math formulas if feel convenient)