technically you need to know how many BTU/hr the logs can put off then match that to the proper tank size. In theory a non-heated propane tank can only put off a certain number of BTU/hr which is relative to the surface area of the liquid propane. (as the propane changes from a liquid to a gas it has to absorb heat from the surrounding environment to do this, if it cant absorb enough heat it starts to gel or freeze up)
to give you an idea of output capacites
BTU/hr output
temp 150 Gal. 250 Gal. 500 Gal.1000 Gal.
40ï½° F 214,900 288,1004 478,800 852,800
30ï½° F 187,900 251,800 418,600 745,600
20ï½° F 161,800 216,800 360,400 641,900
10ï½° F 148,000 198,400 329,700 587,200
0ï½° F 134,700 180,600 300,100 534,500
so while you may be able to run the fireplace off the 100lb tanks (about 23gal) you may find it freezing up on you quickly if the fireplace can put out a lot of BTU/hr
this is why you may have heard of people tossing electric blankets on or wrapping there tanks in black blankets/plastic in extremely (like -20 deg f) weather so they can get enough propane out of the tank to run the furnace.