noob question on f numbers on zoom lens

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Joined
2 Aug 2006
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941
Location
Elloughton, UK
am i right in thinking a 2.8-5.6 lens is no better at max zoom than a 4.5-5.6, so no real point in buying one if i'm usually taking photos at max zoom ?

i just bought a nikon d5100 with a 70-300 4.5-5.6 and just wanted better auto focus / brighter pictures and was wondering best way to go without shelling loads of money out on a prime lens as i'm on a tight budget.
 
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