Solve:

log_e(1+x)^1+x(1-x)^1-x

Prove that:

log_ea - log_eb = (a - b)/a + 1/2 (a - b)²/a² + 1/3 (a - b)³/b³

first question is not so clear

second question can be proved by using expansions of logarithms ... which can be found in any differential calculus books