Com10atorics wrote: Find the set of solutions to the equation $\log_{\lfloor x\rfloor}(x^2-1)=2$ This is $x\ge 2$ and $x^2-1=\lfloor x\rfloor^2$ Which is $\boxed{x=\sqrt{n^2+1}\text{ whatever is integer }n\ge 2}$