Chapter 9 - Review - Page 598: 107

$x=-\dfrac{10,000}{9,995}$

Using properties of logarithms, then, \begin{array}{l} \log(5x)-\log(x+1)=4\\\\ \log\left(\dfrac{5x}{x+1} \right)=4\\\\ \dfrac{5x}{x+1}=10^4\\\\ 5x=10,000(x+1)\\\\ 5x=10,000x+10,000\\\\ -9,995x=10,000\\\\ x=-\dfrac{10,000}{9,995} .\end{array}