Answer
$x = -\dfrac{2000}{1999}$
Work Step by Step
$\log5x-\log(x+1)=4$
$\log \dfrac{5x}{x+1} = 4$
$10^{\log \frac{5x}{x+1}} = 10^4$
$\dfrac{5x}{x+1} = 10000$
$5x = 10000(x+1)$
$5x = 10000x+10000$
$9995x = -10000$
$x= -\dfrac{10000}{9995}$
$x = -\dfrac{2000}{1999}$
