UMVUE for some function $\tau(\theta)$ when $f(x;\theta)=\frac{\ln(\theta)}{\theta -1} \theta^x$

Question

I need to find an UMVUE for some function $\tau(\theta)$ for $X_1, \dots, X_n$ random variables with $f(x;\theta)=\frac{\ln(\theta)}{\theta -1} \theta^x$ where $x\in (0,1)$.
I know that $\sum_{i=1}^{n}X_i$ is a Sufficient and complete statistic, but I don't know which function to choose such that it turns out to be an unbiased estimator.
Any hint?