Final answer:
The value of ln(-274.7) is written as a complex number since the natural logarithm is not defined for negative real numbers. The correct answer is ln(-274.7) ≈ iπ + 5.6157, which is answer choice d.
Step-by-step explanation:
The question relates to finding the value of the natural logarithm of a negative number. The value ln(-274.7) cannot be found directly as the natural logarithm function is only defined for positive real numbers. However, we can use the fact that the natural logarithm of a negative number is a complex number. The formula to express the ln of a negative number is ln|number| + iπ, where i is the imaginary unit and π is pi (approximately 3.14159).
To find ln(-274.7), first find the natural logarithm of the absolute value of -274.7, which is ln(274.7). Using a calculator, we obtain:
ln(274.7) ≈ 5.6157
Since the original number was negative, we add iπ to this result:
ln(-274.7) ≈ iπ + 5.6157
Therefore, the correct answer is d. iπ + 5.6157.