the 7-08 is a fine round and will get you out to some pretty long ranges using good match bullets and is capible of killing Elk when the correct bullet is used. the problem I have found is that very few rifle makers chamber their "accurate" rifles in this round , Ihave found that it is a very un-apperciated calber , its not big and powerfull , doesen't shoot bullets out at near light speed , its just not a "sexy" round anymore.
The good old 308 would also be a good choice as their are many factory LR offerings in this caliber as well as factory ammo loaded for it. The 308 is fully capible fo killing an Elk with a 165-180gr Nosler Partition bullet so long as the ranges are kept reasonable.
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