What resistance is required to run a 6V 75A light with a 12V 2.5A battery?

You can't run a 6V 75A (450W) light off a 12V 2.5A (30W) battery for any significant length of time. That battery is grossly undersized. I think that's supposed to be "0.75A" instead of "75A." I found a 75-watt light bulb on the internet, but 75 amps? You could weld with that much power. And I like the answer right below this one best: just wire two of these bulbs in series. The answer is simple by using the formular called OHM's LAW (V=IxR) The 6V,3/4 amp bulb has (approx) 8 ohms resistance which 'drops' the 6 volts across it. At the same current (thru the SERIES circuit) you need anothe 8 ohm resistance. Unfortunately, the bulb dissipates 4.5 WATTS of power, the same as your 'extra' resistor will have to handle. (Rather WARM!) The easiest trick to do would be to put two 6v bulbs together in series, this will put your 'extra' resistor (the second bulb's filament) inside of a protected glass shell. The second bulb will not waste any more power than the resistor, and will give you twice the light.