What nikon lens has a large value of zoom?

I'm a beginner and I just bought a nikon d3100 but the lens is only 18-55mm. And its zoom is only up to 3x. I want to buy a new lens where I can adjust more zoom.

It depends on how much you want to spend. I'll assume you want it to cost less than your camera!

If you want the widest range for the least cost, add the Nikon 70-300mm f/4-5.6D ED AF (available in good condition used for less than $200 if you look around), and keep the 18-55mm. You'll need to switch lenses depending on what you want to do. If you want new or VR, the latest Nikon 70-300 is the 70-300mm f/4.5-5.6G ED IF AF-S VR Nikkor for $600.

If you want an all-in-one lens with good telephoto range, check out the Sigma 18-250mm F3.5-6.3 DC Macro OS HSM and Tamron 18-270mm F3.5-6.3 Di II VC PZD.

Don't do the Nikon 18-200, in my opinion. Expensive and the 200mm telephoto just does not have much reach. Every time you zoom out to max, you'll wish you had that other 50 or 100mm.

Nikon has a new 18-300 VR, but it is $1000.

Anything longer is going to be really expensive.