12 volt battery voltage step up

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hey, I just took apart an old battery backup surge protector that's battery side wasn't working. I'm assuming it was just a fuse or some other part, as the battery still has a monsterous charge.

I got a really nice 12 volt 4ah/20hr rechargeable battery thats only a little bigger than one of those 6 volt lantern batteries. My question is how did they up the voltage in the circuit to 120 for when power goes out? Did they use a Step-up transformer?

I'd like to make a sort of inverter, kind of like what they use to up the voltage from a car battery to AC 120 for running appliances.

What I would really like to do is only up it to 32 volts @ 2 amps or 40 volts @ 1 amp so I can use this in a 50 watt guitar amp I am building. I also would like to know how to build something to charge the battery with.

So Is this possible? If so, how?

Thanks for any help!
 
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