I ran an experiment where I experimentally (randomly) manipulated $x$ to find out the effect on $y$. Both variables tend to have power law distributions, and this was indeed the case.
I ran some regressions and found out that $x$ is positively correlated with $y$ but $log(x)$ is uncorrelated with $log(y)$. Not only is it insignificant, the point estimate is actually negative. One can make a theoretical case for using either levels or logs.
What should I do for the purposes of an academic paper?