# Why must they be positive?

Number Theory Level 3

$\large 3^m+7=2^n$

Find all positive integer solution $$(m,n)$$ that satisfy the equation above.

Denote $$(m_1, n_1), (m_2, n_2) , \ldots , (m_x, n_x)$$ as all the paired solutions.

What is the value of $$\displaystyle \left(\sum_{k=1}^x n_k \right) \div \left(\sum_{k=1}^x m_k \right)$$?

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