Given a list of numbers each containing 2 prime factors, I wish to make a list of the products of the logs of each factor. For example, given
L = {4,6,9}, I would like to form P = {Log[2]*Log[2],Log[2]*Log[3],Log[3]*Log[3]}.
FactorInteger seems like a questionable route since it would require some work to distinguish squares from numbers with two distinct prime factors.
Any suggestions? Thank you.