Let $$I(x) = \int \sqrt{\frac{x+7}{x}} \ dx$$ and $$I(9) = 12 + 7\log_e 7$$. If $$I(1) = \alpha + 7\log_e\left(1 + 2\sqrt{2}\right)$$, then $$\alpha^4$$ is equal to _____.

Correct Answer: 64

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