My problems #10

Algebra Level 3

The sum of the infinite series

\(\dfrac{\text{log}2}{3}+\dfrac{\text{log}4}{9}+\dfrac{\text{log}8}{27}+\ldots\)

can be expressed as \(\displaystyle\ \dfrac{a\times{\text{log}\ b}}{c}.\) Find \(a+b+c\)

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