Answer
$(0, \infty)$
Work Step by Step
The domain of $e^x$ and $x$ are both all real numbers, so the $\mathbf{j}$ and $\mathbf{k}$ vectors have domain $(-\infty,\infty)$. However, the domain of $\ln x$ is $(0,\infty)$, so the $\mathbf{i}$ vector has domain $(0,\infty)$. The intersection of these domains is $(0,\infty)$.
