What is the inverse z-transform of X(z)=log(1+az-1) |z|>|a|?

1.	What is the inverse z-transform of X(z)=log(1+az-1) \|z\|>\|a\|?
A.	x(n)=(-1)n+1 ( frac{a^{-n}}{n} ), n 1; x(n)=0, n 0
B.	x(n)=(-1)n-1 ( frac{a^{-n}}{n} ), n 1; x(n)=0, n 0
C.	x(n)=(-1)n+1 ( frac{a^{-n}}{n} ), n 1; x(n)=0, n 0
D.	None of the mentioned
Answer» D. None of the mentioned

Discussion

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What is the proper fraction and polynomial form of the improper rational transformX(z)= ( frac{1+3z^{-1}+ frac{11}{6} z^{-2}+ frac{1}{3} z^{-3}}{1+ frac{5}{6} z^{-1}+ frac{1}{6} z^{-2}} )?
What is the inverse z-transform of X(z)=log(1+az-1) |z|>|a|?
What is the inverse z-transform of X(z)= ( frac{1}{1-1.5z^{-1}+0.5z^{-2}} ) if ROC is |z| < 0.5?
What is the inverse z-transform of X(z)= ( frac{1}{1-1.5z^{-1}+0.5z^{-2}} ) if ROC is |z|>1?