Let's say that $Y = \log T = \alpha + \sigma W$. I know that If $W$ has logsitic distribution, the $T$ will have the log-logistic distribution. Also, if $W$ has the standard normal distribution then $T$ has log normal distribution.
My questions are these:
What are the names of the distributions obtained if
(1) $W$ has the exponential distribution
(2) $W$ has the log normal distribution