log transformation

#1
I am trying to understand the relationship between lognormal and normal distribution.
I understand that a variable transformed into a normal distribution by taking the log of it has a lognormal distribution.
I thought that the pdf of this log transformed variable is 1552757041419.png , but looking at Wikipedia, this is the pdf of the lognormal distiribution. I am very confused and would really appreciate an explanation.
 
#3
I am sorry, my question was not very clear. I make another try:

If one takes the log of a log-normal variable the resulting log-variable is normally distributed.
My question is then, what is the pdf of this log-variable?
Is it log [ 1552765603339.png ], where 1552765603339.png is the pdf of a log-normal variable.

I would like to know this because I want to transform a log-normal distribution into a normal distribution to work with it.
 
#4
When taking the log of a lognormally distributed variable (left graph) we get a normally distributed variable (right graph).
1552821621483.png
The probability density function (PDF) of the left graph is: 1552821602539.png
What is the PDF of the right graph?

I have read somewhere that the PDF of the right graph is 1552821602539.png . But I am confused, because this is the PDF of the graph to the left.