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The given expression is \( \ln 40 + \ln 989 \). We can simplify this using the logarithmic property:

\[
\ln a + \ln b = \ln (a \times b)
\]

So,

\[
\ln 40 + \ln 989 = \ln (40 \times 989) = \ln 39560
\]

Now, we compute the natural logarithm of 39560. Using a calculator:

\[
\ln 39560 \approx 10.5829
\]

Thus, \( \ln 40 + \ln 989 \approx 10.5829 \), rounded to four decimal places.

Would you like further details on this? Here are five related questions to expand your understanding:

1. What are some other logarithmic properties besides the sum rule?
2. How does the natural logarithm differ from logarithms with other bases?
3. What real-life applications involve natural logarithms?
4. Can you solve similar logarithmic expressions involving division?
5. How would this calculation change if different bases were used (e.g., base 10)?

**Tip:** Always use the properties of logarithms to simplify expressions before calculating values—it can save time and reduce errors!

Find the value of ln 40 + ln 989. (Round the final answer to four decimal places as needed.)

Solve the logarithmic expression ln 40 + ln 989 using the property ln a + ln b = ln(a * b). The final value is approximately 10.5829 when rounded to four decimal places. Learn more about the properties of logarithms and how to simplify expressions like this.

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