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Statement I gives us that 5^x = 11^y
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my initial logic was that any multiple of 5 will end in five and any multiple of 11 will end in 1 so they are never equal. also 5 and 11 are both primes, this is not an elegant way of explaining it.. but they do not share any prime factors... sp no matter what positve/negative power you put on 11 it will never have a five as one its factors and vice versa.. therefore x=y=0 and 3^xy =1

Statement II gives us that 3^x = 9^y this is true when x=y=0, but it is also true when x=4 and y=2. It might be true for other numbers as well i have no idea how to test or prove it.