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) $a = {1\over 2}, \ b={1\over 4}\quad$
You can find exact solutions to the equation $a^x + b^x = 1$ in special cases like (i) and (ii).