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let f(x)= log((1-x)/(1+x)), find x,y for which f(x)+f(y)=f((x+y)/(1+xy))
Dear Aman f(x) = ln (1-x/1+x)Given that f(x) +f (y) = f(x+y /1 +xy)ln (1-x/1+x) + ln (1-y/1+y) = ln (1 -(x+y)/1 +x+y)ln((1-x)*(1-y)/(1+x)*(1+y)) = ln (1-(x+y)/1+x+y)Removing logAnd. Then on solvingWe get2xy(x+y) = 0Hence xy = 0 or x+y = 0For xy = 0, solution is but obviousFor x+y = 0, x = -yPutting in the given equationln((1+x)*(1-x)/(1-x)(1+x)) = ln1LHS and RHS contradictsHence x = 0 = yAlso1-x >0x 1hencex belongs to (0, 1) RegardsArun (askIITians forum expert)
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