exp(X) has a normal distribution, what is the distribution of X? $\exp(X) $ has a normal distribution of mean $\mu$ and variance $\sigma^2$. What does it say of $X$ ? How do I sample $X$ from its distribution? 

Can I simply apply the natural logarithm after having sampled $\exp(X)$?

Edit - Background:

In a paper (table 2, page 7 - 138)  I can read: $exp(k_{a\_int})$ has a normal distribution N(−2.372, 1.092).
You have $P(X&lt;a)=P(\exp(X)&lt;\exp(a))=\int_{-\infty}^{\exp(a)}$ $f_{\mu,\sigma}(x) dx$ with normal density $f_{\mu,\sigma}$.
You have $P(X&lt;a)=P(\exp(X)&lt;\exp(a))=\int_{-\infty}^{\exp(a)}$ $f_{\mu,\sigma}(x) dx$ with normal density $f_{\mu,\sigma}$.