Chapter 7 Exponential and Logarithmic Functions - 7.6 Solve Exponential and Logarithmic Equations - 7.6 Exercises - Skill Practice - Page 520: 39

$$x=\frac{-3+\sqrt{9+4e}}{2}$$

Using the rules of logarithms to solve the equation, we find: $$\ln \left(\left(x+3\right)x\right)=1 \\ \left(x+3\right)x=e \\ x=\frac{-3+\sqrt{9+4e}}{2},\:x=\frac{-3-\sqrt{9+4e}}{2}$$ Checking for extraneous solutions, we see that only $x=\frac{-3+\sqrt{9+4e}}{2}$ is valid.