Prove the property: log_a(x) + log_a(y) = log_a(xy).

The derivation of the property starts with the basic representation of logarithms as powers. Lets consider a^(log_a(xy)). Then, a^(log_a(xy)) = xy. However, x = a^(log_a(x)) and y = a^(log_a(y)). Therefore, xy = a^(log_a(y)) * a^(log_a(x)) = a^(log_a(x) + log_a(y)). Hence, log_a(x) + log_a(y) = log_a(xy).