Yes you can with a Sony A5100 or A5000 camera.
Fast zoom lenses are expensive and bulky, killing the whole point of a compact digital camera. A nifty-fifty lens like the Sony 35mm f1.8 is great for still photos, because you can easily crop to do post zoom. For video, however, post zooming means quality loss.
Fortunately, almost all mirror-less cameras now can do loss-less zoom for video and Sony is the best on this regard. With an Sony A5100 (or A5000), you may use its zoom rocker to zoom losslessly and continuously up to 2x. For example, with the 35mm lens, you may zoom from 35mm to 70mm as you see in this video:
A6000 does not have a zoom rocker, therefore you cannot zoom a prime (non-zoom) lens. You still can zoom any zoom lenses though, for example, you can make the 16-50mm kit lens become a true 16-100mm.
The 35mm lens features OSS (optical steady shoot), ideal for video. Panasonic's 25mm f1.4 does not have OIS (optical image stabilizer), hence not suitable for video and why I jumped the wagon.
Although such zooming seems like digital zoom, it is not. Video does not use all the pixels of the sensor, so this 2x cropping
does not lose any resolution. Noise might be higher though, due to less
condensation of pixels.