Logarithmic Polynomial?

Algebra Level 5

\(P(x)\) is a polynomial with degree of 5. Given that \( P(1)=0\), \(P(3)=1\), \(P(9)=2\), \(P(27) =3\), \(P(81)=4\) and \(P(243)=5\). What is the coefficient of \(x\) in the polynomial? If the answer can be expressed in the form of \(\frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers, find the value of \(a+b\)?

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