@surfmom Just a couple of extra details as @xelas has covered most of the points
1) The EF 70-300 L is not compatible with any of Canon's extenders so you would have to get a third party extender if you got this lens and wanted more reach. The lens itself is sharp and has fast AF so well worth considering if the animals will be close such as in a zoo or on private reserves where they could get you close to the animals.
2) Generally Canon extenders are preferred as Canon makes their lenses of the same era compatible with those extenders so you get the best AF. The best combination for safaris is definitely the 100-400 mark 2 with the 1.4x mark 3. They work brilliantly together especially with the 7D2 which has Canon's fast AF even with this extender attached. The older 100-400 mark 1 focusing slows down hugely with extenders of all varieties and ages.
3) I have used the 70-200 f2.8 mark 1 plus 1.4x mark 2 on safari which gives you an effective 100-280 f4 and it was OK at water holes from hides but not so good on drives where we were restricted to the roads. The 70-300 L would be a better option.
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