$$ e^Z \sim \mathrm{Lognormal} \iff Z \sim \mathrm{Normal} $$
Why would we call the exponential of a normal distribution log-normal? The fact that the log of a lognormal is normal seems bizarre. It would make more sense if the log of an expnormal was normal or the exp of a lognormal was normal.
I am thinking about as Log(Normal), but that gives the opposite of the correct intuition, so what is the correct way to think about it? "The Log of this is Normal"? Is there any history or analogous terminology that can guide me to the right intuition here?