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! 

It works as for most products of two quantities: you have $\log x \log 2x < 0 $ if they ($ \log x$ and $ \log 2x$) are of opposite signs
This amounts to: $0<x<1$ and  $2x>1$, or $x>1$ and  $0<2x<1$, hence $x\in ]\frac{1}{2},1[$, or $\emptyset$ (respectively), hence the solution is $x\in ]\frac{1}{2},1[  \cup \emptyset =  ]\frac{1}{2},1[ $.
