Question

Values of $x$ satisfying the equation, ${\log }_{10}\sqrt{1+x}+3{\log }_{10}\sqrt{1-x}={\log }_{10}\sqrt{1-x^2}+2$ is

• A. $0<x<1$
• B. $-1<x<1$
• C. $-1<x<0$
• D. None of these

Answer 1

The correct option is D None of these

Given expression is valid when $x>-1$, $x<1$, $x^2<1$
Therefore, $x\in (-1,1)$
But for $x=0$, L.H.S$\ne$R.H.S
Thus $x\in (-1,1)-0$
Ans: D