Just a Simple Logarithm

Algebra Level 3

If (logab)+(logab)2+(logab)3+........=2 (\log_{a} {b}) + (\log_{a} {b})^2 + (\log_{a} {b})^3 + . . . . . . . . = 2, and n=a23 n = a^{\frac{2}{3}}, then :

logab+logbn=....\log_{a} {b} + \log_{b} {n} = . . . .

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