Newbie Lens/Focal Length Question

Hello,

Please correct me where I am wrong.

I understand that the focal length of the lens can be varied and in
doing so you change the "zoom" of the lens.

I understand that 50mm sees things pretty much as I see it. I have a
1.6x crop so to see things through the camera as I see it, I 'd shoot
at 50/1.6= ~30mm.

If I wanted 10x zoom, would I be looking for an effective focal length
of 500mm?

Thanks