When you read "digital zoom" think of merely cropping out the edges of
your image then interpolating the remaining pixels to fill out the
frame.  This is the same process a good photo editing program is able to
do only with digital zoom it is done in camera instead of at your
workstation. My advice is to ignore any digital zoom feature and look
instead at the optical zoom specifications.  Put your money in the lens
and sensor size not in the parlor tricks.  Always capture at max
resolution and do your magic with Photoshop.  Don't have Photoshop? In
many digital camera's you can crop after the fact with the advantage of
selecting the approximate area of interest.  Of course if you are
shooting stuff for sale on eBay or something, that is different.  Save
yourself the extra step of resizing your image and shoot what you need.

Note that the "X" does not refer to the total magnification only the
ratio.  If you have a 3x optical and a 7x digital you have change of 21X
from wide to tele. The associative law of multiplication states that you
can factor the optical and the digital any any order you want.   If your
optical takes you to a 114mm 35mm equivalent then 7 X 114 is a 798mm
equivalent for a 35mm.  But if you think that by so doing you will
achieve the same results as using a real telephoto, you are being fooled.

A while back a poster made a good case that the zoom lens of these
digital viewfinder cameras was unable to resolve images beyond about 2Mp
anyway.  In other words the lines per mm the lens is able to resolve is
less than the space between the pixels on the sensor. I did his math and
his figures seemed right.  You can buy a 5Mp sensor but all you are
doing with it is sensing the same image only using up more pixels
needlessly.  Point is if you want a lot of Mp then get a camera with a
larger sensor.