Chapter 3: Exam Question ( Related to Functions of Continuous Random Variables)

In the exam question, can someone clarify how the limits of the random variable Y is determined: It is given as

"Since X can take values in the range 0 < X < 1, Y can take values in the range 0 < Y < infinity"

If I substitute Y = - Theta * ln X, and 0<x<1 in it, the limits must be (-1 and 0) or if my approach is wrong, can someone tell me how this limits are exactly determined...

 

Ln1 =0 but ln0 tends to -ve infinity, then after multiplying by -theta limits will be 0 to infinity

 

Thank You.