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  4. Number of solution satisfying the equation log x(1-x)=2 log x(x+1), is

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Q. Number of solution satisfying the equation $\log _x(1-x)=2 \log _x(x+1)$, is

Continuity and Differentiability

Solution:

Given, $\log _{ x }(1- x )=2 \log _{ x }( x +1) $
$\Rightarrow(1-x)=(x+1)^2 \Rightarrow 1-x=x^2+2 x+1 \Rightarrow x^2+3 x=0 \Rightarrow x=0$ or -3 (Reject both)
Hence, no solution exist.