Solve the equation $$a^x + b^x = 1$$ where $0< a, b < 1$ and $a + b < 1$, in the special cases:
(i) $a = b\quad$ (ii) $a = {1\over 2}, \ b={1\over 4}\quad$ (iii) $a = {1\over 2}, \ b={1\over 3}$ .