MLEs in a Lognormal Model from Log-Summaries

Suppose positive holding-period multipliers are modeled as lognormal: if $X\sim \mathrm{Lognormal}(\mu,\sigma^2)$ then $\log X\sim N(\mu,\sigma^2)$. For a sample of size 12, you are given $$\overline{\log X} = 0.3, \qquad \sum_{i=1}^{12}(\log X_i-0.3)^2 = 10.8.$$ Find the MLEs of $\mu$ and $\sigma^2$, and then give the fitted median of $X$.