1. **State the problem:** Evaluate $\ln\left(e^{\sqrt{3}}\right)$.\n\n2. **Recall the logarithm rule:** For any positive number $a$ and exponent $b$, $\ln\left(e^b\right) = b$ because the natural logarithm $\ln$ is the inverse of the exponential function with base $e$.\n\n3. **Apply the rule:** Here, $b = \sqrt{3}$, so\n$$\ln\left(e^{\sqrt{3}}\right) = \sqrt{3}.$$\n\n4. **Final answer:**\n$$\boxed{\sqrt{3}}.$$