Question

Solve the following systems of equations.
$log\sqrt{5-x}+log2=log(x+3),x^2+7x-8=0$

Answer 1

$log\sqrt{5-x}+log2=log(x+3)$ $x^2+7x-8=0$

$log\left(2\sqrt{5-x}\right)=log(x+3)$

$\Rightarrow 2\sqrt{5-x}=x+3$

$\Rightarrow 4(5-x)=x^2+9+6x$

$\Rightarrow x^2+10x-11=0$

$\Rightarrow (x+11)(x-1)=0$

$x=-11,1$

$(x+8)(x-1)=0$

$\Rightarrow x=1,-8$

$=x=1$ is the common solution