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 \[\log_n x - \log_n y = 1?\]
