# 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 \( \displaystyle \left(\sum_{k=1}^x n_k \right) \div \left(\sum_{k=1}^x m_k \right) \)?