Having problems with mac software

So I upgraded to iOS 7 on my iphone 4s and I'm trying to plug it in to my iTunes, but iTunes said I need version 11.1 for my phone now so I tried to download that but to download that I need mac os x 10.6.8 or later so I tried to download that but I need 10.6 or later to download it and that costs 20 bucks. Is paying for os x 10.6 the only way to solve my problem? I don't know much about software so some help would be great! I'm also trying to save a trip to the apple store.

You could download an alternative program, instead of iTunes. Officially, there's no way around paying the $20.

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