$-\log X_i$ is exponential with rate $\theta$, so the sum is Gamma$(n,\theta)$

Suppose $X_1,\dots,X_n$ have the pdf $f(x\mid\theta)=\theta x^{\theta-1}$, $0<x<1$, $\theta>0$. The distribution of $\sum_{i=1}^n-\log X_i$ is: