If $X$ has the density function
f_\vartheta (x) = \Big \{ \begin{array}{cc} (\vartheta - 1)x^{-\vartheta} & x \geq 1\\ 0 & otherwise \end{array}
How can I see that $\log X \sim Exp(\vartheta - 1)$? I had the idea to look at $f(\log x)$ but I think that's not right. Many thanks for your help!