Just a Simple Logarithm

Algebra Level 3

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

\[log_{a} {b} + log_{b} {n} = . . . . \]

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