To solve the problem of finding the natural logarithm of 40, we denote it as [tex]\(\ln 40\)[/tex].
1. First, determine the natural logarithm of the number 40:
[tex]\[
\ln 40 \approx 3.6888794541139363
\][/tex]
2. To provide the answer rounded to four decimal places, look at the fifth decimal digit to decide if rounding is needed. If the fifth digit is 5 or greater, the fourth digit increases by one; otherwise, it stays the same.
3. Given [tex]\(\ln 40 \approx 3.6888794541139363\)[/tex], the fifth decimal digit is 7.
4. Since 7 is greater than 5, we round up the fourth digit:
[tex]\[
\ln 40 \approx 3.6889
\][/tex]
Therefore, rounded to four decimal places, the natural logarithm of 40 is [tex]\(\boxed{3.6889}\)[/tex].
