Definition: a random variable Y is defined as Lognormal distributed if its logarithm is Normal distributed.

That means, given X=Log(Y) with

then

Well, I’m having very hard time to prove this. How can I go from the PDF of X to the pdf of Y?

In a previous post, Tukeywilliams says "use the transformation theorem to get the pdf of the lognormal". I tried unsuccesfully...

I would appreciate any help. Thanks!