I have a battery powered device.
I'm sick of changing the 3 AA batterys every second day.
I have some old modem power supplys which supply 6V.
It smells like "voltage divider". You put the device in series with a resistor and connect them to the modem power supply.
The formula should be:
Rvoltagedivider=(Upowersupply - Udevice)/I
I should be the maximum supported current of the device. It doesn't have it printed on, so I took the specification of the power supply (200mA), hoping it will neither be too much or not enough for the device
The resistor won't regulate the voltage though. You can use the resistive divider when the current is unchanging and well known, like a heater, light bulb, rechargeable battery, or LED. Also, unless the power supply has a regulator in it, the source voltage will vary quite a bit.
You need a voltage regulator. 4.5v would be unusual so you probably want an adjustable one like a 317.