Can we choose integers \(x\) and \(y\) so that:

\[\log_6 x +\log_6 y =1?\]

How many different ways are there to do this?

How about using \(\log_{12}\)?

How about using \(\log_{24}\)?

How might your answers change if the equations were instead of the form \[\log_n x - \log_n y = 1?\]