For a camera with a 1.5x crop factor the lens would be 34/1.5 or 24mm (rounded up) to 80/1.5 or 54mm so a 1.5x crop factor would need a 24-54mm range.

For a camera with a 2x crop factor it would be 34/2 or 17mm to 80/2 or 40mm so the lens would be 17-40mm.

Smaller sensors allow better power management, smaller & lighter camera and lens construction and improved optical designs for lenses to be used with sensors (for design reasons image sensors need more direct or "straighter" light paths than film). The sensors also generate less heat which may cause image deterioration when a camera is used continuously.

The advantage of larger sensors is that they can have physically larger "pixels" so they are less likely to have a bleed over from adjacent pixels. The bleed causes image deterioration in the form of "noise".

Typical crop factors are in the range from 1.3 – 2.0. Most camera companies use whatever they want but some cameras have adopted a standard called Four/Thirds which has a 2x crop factor.

Hope this helps.
Email if you have more specific questions.

EDIT: Additional info, the Olympus 14-45 "kit" lens is roughly equivalent to a 28-90mm and would be very comparable. I have a lightly used one for sale. If you are interested contact me via email.