Answer
$x=\frac{5}{e^3-1}$ or $x\approx 0.262$
Work Step by Step
$\ln x-1=\ln (5+x)-4$ (Move $-1$ and $\ln (5+x)$ and change their signs)
$\ln x -\ln (5+x)=1-4$ (Use the property $\ln \frac{a}{b}=\ln a-\ln b$)
$\ln \frac{x}{5+x}=-3$ (Take the exponent)
$\frac{x}{5+x}=e^{-3}$
$\frac{x}{5+x}=\frac{1}{e^3}$ (Cross multiply)
$e^3 x=5+x$ (Move $x$ and change the sign)
$e^3x-x=5$ (Factor out $x$)
$(e^3-1)x=5$ (Divide by $e^3-1$)
$x=\frac{5}{e^3-1}$
$x=0.26197....$
$x\approx 0.262$
Thus, $x=\frac{5}{e^3-1}$ or $x\approx 0.262$.
