Question

The solution set of the equation ${\log }_{5/(x^2+6)}(13+4x^2-4x)={\log }_{7+\sqrt{x}}(-2x-x^2)$ is

• A. $9$
• B. $16$
• C. $81$
• D. none of these

Answer 1

Answer: (D)

none of these

First check the domain of the given equation,
(i) $x>0$
(ii)$-2x-x^2>0\Rightarrow x^2+2x<0\Rightarrow x(x+2)<0\Rightarrow x\in (-2,0)$
Clearly using (i) and (ii) domain is $\varphi$(empty set)
Hence,there will not be any solution for the given equation.