  The classic double bubble theorem says that the least-perimeter way to
enclose and separate two prescribed volumes in $\mathbb{R}^N$ is the standard
double bubble. We seek the optimal double bubble in $\mathbb{R}^N$ with
density, which we assume to be strictly log-convex. For $N=1$ we show that the
solution is sometimes two contiguous intervals and sometimes three contiguous
intervals. In higher dimensions, we think that the solution is sometimes a
standard double bubble and sometimes concentric spheres (e.g. for one volume
small and the other large).
