baryonic acoustic oscillations

In what way do BAOs work as a geometrical distance measurement? What happens to BAOs in nonlinear structure formation? What assumptions concerning biasing does one do? bonus question: is there an intuitive argument why the BAOs get destroyed in nonlinear structure formation?

extra bonus: What’s \(\log_\mathrm{i}(\sqrt[\mathrm{i}]{\mathrm{i}})\) with \(\mathrm{i} = \sqrt{-1}\)?