Binocular zoom and lens focal length just aren't equivalent and can't be converted in any meaningful way.

A camera lens is an image-forming system. It has a focal length. Binoculars and telescopes (with eyepiece in place) are "afocal" systems — there's no focal plane onto which the image converges. Individual elements (or even groups) within the binoculars have a focal length, but they are arranged together so that they produce magnification, but their "effective focal length" is infinite.

In photography, we often use focal length as a stand-in for field of view, because — for a given film or sensor size — there's a direct correlation. And the phrase "equivalent field of view" is used when comparing different sensor sizes, with 35mm-film-equivalent being the most common (see crop factor).

Unfortunately for your wish here, there's no way to tell this from the two numbers normally given for binoculars — the objective size (diameter of the front element, basically) and magnification. The angle of view is given as a separate specification, and from that you could simply work back to what camera lens would have a similar field of view. But you don't get that from the 10× or 30× alone, nor from something like 10×50. You'll need to look in the specs for a particular model of binoculars to get this information.

For example, these Pentax 8×40 binoculars have (not surprisingly) 8× magnification and a 40mm objective lens. They also have a 6.3° angle of view. On a "full-frame" DSLR, this is the diagonal angle of view of approximately a 400mm lens. But these Olympus 8×40 binoculars have the same magnification and objective size, yet an 8.2° angle of view — similar to a 300mm on a full-frame DSLR.

(Note that some binoculars will give an "apparent" field of view, which is the actual FoV multipled by the magnification. This is useful when comparing binoculars of different magnification, but isn't what you're looking for the purpose here. Look deeper in the specifications — it may be labeled actual field of view.)

Note that if you're looking through the viewfinder and comparing to binoculars side by side, that's yet another thing — see What does "viewfinder magnification" mean? and What is it called when an object appears to be the same size with the eye and through the camera viewfinder? for some details. But, assuming your goal is really to take pictures and not just replace your binoculars with a camera, this is a curiosity rather than something to really worry about.