How to work with Log-transformation?
Taking the log doesn't result in a normally-distributed target; it would tend to if the target was log-normally distributed, and you have something normalish there, not quite. But, this distribution isn't actually what matters.

What taking the log does is change your model of how errors arise when fitting a regressor. You're now saying that the target values are $e^{P + \epsilon}$ where $P$ is your model's prediction and $\epsilon$ is Gaussian noise. Or: $e^P e^\epsilon$. That part directly interacts with the assumptions in your regressor. 

So what you're finding is that on average the predictions are wrong by a factor of 7.39, not +/- $7.39.

What you really want to do is evaluate MAE on actual target values vs $e^P$ . You probably have a better model but not that much better.