Statement 1: If
`log(1-x+x^(2))=a_(1)x+a_(2)x^(32)+a_(3)x^(3)+..`
then `a_(3)+a_(6)+a_(9)+..=2/3log_(e)2`
Statement 2: `1-1/2+1/3-11/4+1/5-1/6+..=log_(e)2`

Explanation

To solve the given problem, we need to analyze both statements one by one.

### Statement 1:
We are given that:
\[ \log(1 - x + x^2) = a_1 x + a_2 x^2 + a_3 x^3 + \ldots \]
We need to find \(a_3 + a_6 + a_9 + \ldots\) and check if it equals \(\frac{2}{3} \log_e 2\).
...