SOLUTION: Find the pair of integers (a,b) for which 2^(a+1) + 2^a = 3^(b+2)

SOLUTION: Find the pair of integers (a,b) for which 2^(a+1) + 2^a = 3^(b+2) - 3^b

Question 1199910: Find the pair of integers (a,b) for which 2^(a+1) + 2^a = 3^(b+2) - 3^b
Answer by greenestamps(13330) (Show Source): You can put this solution on YOUR website!

Simplify using greatest common factors on both sides:

Both expressions are prime factorizations, so the exponents on like prime factors must be the same: a=3 and b=1

ANSWER: (a,b) = (3,1)

CHECK:
2^4+2^3 = 16+8 = 24
3^3-3^1 = 27-3 = 24

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