3. In the Cartesian coordinate system, a line $l$ passing through the origin $O$ intersects the curve $y=\mathrm{e}^{x-1}$ at two distinct points $A$ and $B$. Parallel lines to the $y$-axis are drawn through $A$ and $B$, intersecting the curve $y=\ln x$ at points $C$ and $D$. The slope of the line $CD$ is $\qquad$.
3. 1 .

Given the line $l: y=k x(k>0)$, and it intersects the curve $y=\mathrm{e}^{x-1}$ at different points $A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right)$.
$$
\begin{array}{l}
\text { Hence } k x_{1}=\mathrm{e}^{x_{1}-1}, k x_{2}=\mathrm{e}^{x_{2}-1} \\
\Rightarrow x_{1}=\frac{1}{k} \mathrm{e}^{x_{1}-1}, x_{2}=\frac{1}{k} \mathrm{e}^{x_{2}-1} \\
\Rightarrow k_{C D}=\frac{\ln x_{1}-\ln x_{2}}{x_{1}-x_{2}} \\
\quad=\frac{\ln \frac{1}{k} \mathrm{e}^{x_{1}-1}-\ln \frac{1}{k} \mathrm{e}^{x_{2}-1}}{x_{1}-x_{2}}=1 .
\end{array}
$$