Answer
Graphically: $x=1.482$
Algebraically: $x=1.482$
Work Step by Step
Let $y_1=2\ln (x+3)$ and $y_2=x$.
The graph using graphing utility is as shown.
The intersection point is at $(1.482,3)$.
Thus, the solution is $x=1.482$.
Solving algebraically, divide both sides of the equation by $2$:
$$2\ln (x+3)=3$$ $$\ln (x+3)=\frac{3}{2}$$
Rewriting the equation in exponential form where $\ln (x)=y$ is equivalent to $x=e^y$:
$$x+3=e^{\frac{3}{2}}$$ $$x=e^{\frac{3}{2}}-3$$ $$x=1.482$$
Thus, the solution is verified algebraically.
