Question

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

• A. zero
• B. one
• C. two
• D. more than 2

Answer 1

Answer: (A)

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