Question

The number of solutions of the equation $\log _{2}\left(x^{2}+2 x-1\right)=1$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

Given $\log _{2}\left(x^{2}+2 x-1\right)=1$
$\Rightarrow \log _{2}\left(x^{2}+2 x-1\right)=\log _{2} 2$
$\Rightarrow x^{2}+2 x-1=2$
$\Rightarrow x^{2}+2 x-3=0$
$\Rightarrow x^{2}+3 x-x-3=0$
$\Rightarrow x(x+3)-1(x+3)=0$
$\Rightarrow (x+3)(x-1)=0$
$\Rightarrow x=1,-3$
Since, $x=1$ and $x=-3$ are satisfy the given equation therefore the number of solutions of the equation are two.