What's the mathematical relationship between the system volume and the master volume control on my speaker?

What's the mathematical relationship between the system volume and the master volume control on my speaker?
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Answer :

I don’t think it’s possible to answer, since you’re measuring apples and oranges. Software volume is controlled differently than hardware volume. (This is why you should always control volume with an analog dial rather than with software; lower software volume degrades signal and causes downsampling.)
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