I have a question regarding the log normal and normal distribution.

What I think is that if Y has a normal distribution then X=log(Y) has log normal.

Specifically in Wolfram: http://mathworld.wolfram.com/LogNormalDistribution.html is written about lognormal:

"A continuous distribution in which the logarithm of a variable has a normal distribution." which is a bit unclear: of what kind of variable?.

In wikipedia about log normal:

"In probability theory, a log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. If Y is a random variable with a normal distribution, then X = exp(Y) has a log-normal distribution; likewise, if Y is log-normally distributed, then log(Y) is normally distributed"

which is not the case I think.. Am I not correct?

So what is correc?

If Y is normal log(Y) is lognormal?

or

If Y is normal exp(Y) is lognormal?

If the correct is the first one then wiki is wrong?

Thanx in advance for any answers!!