b/c survival time (T) is positive.
In the survival analysis model, Log T = b0 + b1*X1 + ... + bn*Xn + σε,
where b0, b1, ..., bn are regression coefficients of interest, σ is a scale parameter and ε is the random disturbance term.
If ε~logistic dist, then T~log logistic dist.
If ε~Normal dist, then T~log Normal dist.
If ε~gamma dist, then T~log gamma dist.
The reason why we take log of T is obviously considering the fact that the survival time is always positive.