PDF distribution of ln(x) when x has normal distribution

[minm]

Hi All,

I'm wondering if ln(x) has any know distribution when x is a normal random variable?
Also, is there any distribution for x that generate a known distribution for ln(x)?

Thanks,

 

[fzero]

You might want to look at http://en.wikipedia.org/wiki/Random_variable#Functions_of_random_variables There is a derivation for $$f_Y$$ in terms of $$f_X$$ when $$Y = g(X)$$ is either invertible or has a countable number of roots.