The positive integers a, b, c are the smallest that satisfy the equations:

a^5 = 3b^4 = 2c^3

If \ln{a}+\ln{b} + \ln{c}=p\ln{2}+q\ln{3}, where p and q are positive integers, then what is p+q?

Source: Ritangle, Stage 1, 2021

Note: \ln{x} means the ‘natural (base e) logarithm‘ of x.

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