Problem

Source:

Tags: Comc, 2017 COMC



Source: 2017 Canadian Open Math Challenge, Problem A4 Three positive integers $a$, $b$, $c$ satisfy $$4^a \cdot 5^b \cdot 6^c = 8^8 \cdot 9^9 \cdot 10^{10}.$$ Determine the sum of $a + b + c$.