$\ln\mathscr{L} = \ln(1 - \Phi(x)) + \ln(\Phi(x))$
Is there any general method to maximize $\ln\mathscr{L}$ for argument $\Phi(x)$? In other words, to do $\arg\limits_\Phi \max (\ln(1 - \Phi(x)) + \ln(\Phi(x))) ?$
p.s. solved by Clement C. in his comment.