From the uploaded image, we need to evaluate the following expressions and round the answers to the nearest thousandth:

1. $\ln \sqrt{13}$
2. $\log 27.2$

Let me compute these for you:

1. $\ln \sqrt{13}$:
   Using the property of logarithms:
   $\ln \sqrt{13} = \ln (13^{1/2}) = \frac{1}{2} \ln 13$
   Approximation: $\ln 13 \approx 2.564949$
   $\ln \sqrt{13} = \frac{1}{2} \times 2.564949 = 1.282475$
   Rounded to the nearest thousandth: $\ln \sqrt{13} \approx 1.282$

2. $\log 27.2$:
   Use the base-10 logarithm property:
   $\log 27.2 \approx 1.43457$
   Rounded to the nearest thousandth: $\log 27.2 \approx 1.435$

Final Results:

1. $\ln \sqrt{13} \approx 1.282$
2. $\log 27.2 \approx 1.435$

Would you like a detailed explanation of the steps?

Here are 5 related questions to expand your understanding:

1. How do natural logarithms ($\ln$) differ from base-10 logarithms ($\log$)?
2. How do the properties of logarithms simplify complex expressions?
3. Can logarithms of negative numbers or zero be evaluated? Why or why not?
4. What is the practical significance of $\ln$ in real-world applications?
5. How would you compute $\log$ or $\ln$ without a calculator?

Tip: Always apply logarithmic properties to simplify expressions before calculating, as this reduces potential errors!