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If you say it is from 35mm to 105mm (in optical zoom this is like 1x to 3x correct?) Focal length ratio = optical zoom factor, thus 105 mm.
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I don't know where your camera's zoom range begins, but it's likely that in 35mm film terms, it's somewhere between 28 mm and 38 mm. A 3x optical zoom factor with a 35mm-equivalent lower focal length would imply a 105mm-equivalent upper focal length.
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Isn't that the same thing as saying 3x(multiplied by 2.6x) gives you 7.8x zoom?
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A zoom lens that had a 7.8x zoom range would give you the equivalent of a (35 - 273) mm range
without the need to change lenses, or to attach and detach telephoto converters. A teleconverter may give you a 7.8x total range, but you will need to attach/detach the teleconverter as you cross the middle of it.