Log of the mean of a standard lognormal

If $\ln X$ has a standard normal distribution, what is the value of $\ln\left(\mathbb{E}[X]\right)$?

$1/2$. Write $X=e^Z$ with $Z\sim N(0,1)$. The normal moment generating function gives $\mathbb{E}[e^{Z}]=e^{1/2}$, so the log of the mean is $\tfrac12$ (not $0$, which is the mean of the log).