Logs in equivalent forms including proof

Question

Prove logxxy -2logxy = 1 - logxy 



Answer 1

This is very unclear the way it is typed, but the only way it makes sense (and is true) is if I rewrite it as:

log_x(xy) - 2 log_x(y) = 1 - log_x(y)

Properties of logs say we can expand:

log_x(x) + log_x(y) - 2 log_x(y)

By definition, log_x(x) = 1

So this becomes 1 + log_x(y) - 2 log_x(y) and this becomes 1 - log_x(y)