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The sum of the infinite series
log23+log49+log827+…\dfrac{\text{log}2}{3}+\dfrac{\text{log}4}{9}+\dfrac{\text{log}8}{27}+\ldots3log2+9log4+27log8+…
can be expressed as a×log bc.\displaystyle\ \dfrac{a\times{\text{log}\ b}}{c}. ca×log b. Find a+b+ca+b+ca+b+c
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