# 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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