SOLUTION: 2^(x+1)+2^x=3^(y+2)-3^y where x and y are elements of integers. Find x

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Question 1153078: 2^(x+1)+2^x=3^(y+2)-3^y where x and y are elements of integers. Find x
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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Simplify the given equality step by step


    2%5Ex%2A%282%2B1%29 = 3%5Ey%2A3%5E2-3%5Ey,


    2%5Ex%2A3 = 3%5Ey%2A%289-1%29


    2%5Ex%2A3 = 8%2A3%5Ey.


With integer x and y, taking into account uniqueness of factorization of integers into a product of prime numbers,

it implies  x= 3  and  y= 1.    ANSWER