Multiplying two logarithms (Solved) I was wondering how one would multiply two logarithms together? 
Say, for example, that I had:
$$\log x·\log 2x < 0$$
How would one solve this? And if it weren't possible, what would its domain be?
Thank you!
(I've uselessly tried to sum the logs together but that obviously wouldn't work. Was just curious as to what it would give me)
EDIT: Thank you everyone for the answers! 

There is no particular rule for the product of logarithms, unlike for the sum.
Applying the latter, you can rewrite
$$\log(x)\log(2x)=\log(x)(\log(x)+\log(2))=t(t+\log(2))$$
and proceed as usual to find the domain of $t$. Then $x=e^t$.
