Construct a symmetric two-sided $\displaystyle (1-\alpha)100\%$ confidence interval for the unknown parameter $\displaystyle \beta > 0$ in a $\displaystyle Beta(1,\beta)$ sample.

The hint is to find the MLE of $\displaystyle \beta$ and determine the distribution of $\displaystyle -log(1-X)$ for a $\displaystyle Beta(1,\beta)$ random variable $\displaystyle X$