= 1 + lnx -1 - ln(1-x) = lnx - ln(1-x) = ln(x/(1-x)) = 0 for a min then e^0 = x/(1-x) 1 = x/(1-x) 1-x = x x = 1/2 Proof: confirmed by Wolfram http://www.wolframalpha.com/input/?i=plot+y+%3D+x+ln+x%2B%281-x%29ln%281-x%29
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