Why must they be positive?

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

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

Denote (m1,n1),(m2,n2),,(mx,nx) (m_1, n_1), (m_2, n_2) , \ldots , (m_x, n_x) as all the paired solutions.

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

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