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A. 8^x+1 = 16^x-3
2^3(x+1) = 2^4(x-3)
3x + 1 = 4x - 12
3x - 4x = -12 - 1
-x = -13
x = 13
B . 2^2x - 6 (2^x+1) + 32 = 0
2^2x - 12^x+1 + 32 = 0
2x + 5 = x + 1
2x - x = 1 - 5
x = -4