My problems #10

Algebra Level 3

The sum of the infinite series

log23+log49+log827+\dfrac{\text{log}2}{3}+\dfrac{\text{log}4}{9}+\dfrac{\text{log}8}{27}+\ldots

can be expressed as  a×log bc.\displaystyle\ \dfrac{a\times{\text{log}\ b}}{c}. Find a+b+ca+b+c

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