Can't turn ON transistor from output of comparator?
Your circuit needs to look something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

Comparator outputs are typically open-collectors, so they'll sink current in order to output a "0".  You need a pull-up in order to have the output actually go high, feeding current into the base of your switching transistor.  R1 needs to be high enough so you don't cram too much current into the comparator when it's trying to pull low (20 mA might be absolute max, so go with a bit less than that), but low enough to fully saturate Q2 in order to drive whatever load you're planning on using.  R2 can (probably should) be zero.

As Ignacio pointed out, the base of Q2 will stay around VBE(sat), typically 0.6-1.0 V for most BJTs.  If you manage to exceed that by very much, you'll destroy the device.  The voltage isn't really relevant anyways; BJTs are current devices.