1. The problem is to solve the equation $$5 \ln x = 10$$ for $x$. 2. Recall the property of logarithms: if $a \ln x = b$, then $\ln x = \frac{b}{a}$. 3. Apply this property to the equation: $$5 \ln x = 10 \implies \ln x = \frac{10}{5} = 2$$ 4. To solve for $x$, recall that $\ln x$ is the natural logarithm, so $x = e^{\ln x}$. 5. Substitute $\ln x = 2$: $$x = e^2$$ 6. The approximate value of $e^2$ is about 7.389. Therefore, the solution is: $$x \approx 7.389$$