Building blocks

## Problem 2

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 $\log_n x - \log_n y = 1?$