1. **State the problem:** We want to find the limit $$\lim_{n \to \infty} \frac{\ln m}{\ln n}$$ where $m$ is a constant and $n$ approaches infinity. 2. **Recall the properties:** The natural logarithm function $\ln x$ grows without bound as $x \to \infty$, but $m$ is a constant, so $\ln m$ is a fixed number. 3. **Analyze the expression:** Since $\ln m$ is constant and $\ln n \to \infty$ as $n \to \infty$, the fraction becomes $$\frac{\text{constant}}{\text{increasing without bound}}$$ 4. **Evaluate the limit:** As the denominator grows without bound, the fraction approaches zero: $$\lim_{n \to \infty} \frac{\ln m}{\ln n} = 0$$ 5. **Conclusion:** The limit is zero because the denominator grows infinitely large while the numerator remains constant.