Lognormal moments and variance of the log

Let $X$ be a continuous random variable with probability density function $f(x) = \frac{1}{\sigma x \sqrt{2\pi}} e^{-\frac{1}{2} (\frac{\log_{e} x - \mu}{\sigma})^2}, \; x > 0$, where $\mu \in \mathbb{R}$, $\sigma > 0$. If $\log_{e} (\frac{E(X^2)}{(E(X))^2}) = 4$, then $\operatorname{Var}(\log_{e} X)$ equals