Answer
See below
Work Step by Step
$$4^{x+1}=2^{2x+2}\\8^{3x}=2^{9x}\\4^{x+1}=8^{3x}\\2^{2x+2}=2^{9x}\\2x+2=9x\\7x=2\\x=\frac{2}{7}$$
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