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Solve in integer numbers 2^(x+1) + 2^x = 3^(y+2) - 3^y
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Left side of the given equation is 2*2^x + 2^x = 3*2^x.
Right side of the given equation is 9*3^y + 3^y = 8*3^y.
So, the given equation is
3*2^x = 2^3*3^y.
Due to uniqueness of decomposition integer numbers into the product of prime numbers,
from the last equation we conclude
x = 3, y = 1.
ANSWER. x = 3; y = 1.
Solved.
