Question

If \( n = 1999 \), then \( \sum_{i=1}^{1999} \log x_i \) is equal to

• A. \( \log 1999 \)
• B. 0
• C. \( -1 \)
• D. \( \log 1999! \)

Hint:

The sum of logarithms can be simplified to the logarithm of the product of the terms.

Answer 1

The Correct Option is D

Step 1: Using logarithmic properties.
The sum of logarithms can be expressed as the logarithm of the product. Therefore, \( \sum_{i=1}^{1999} \log x_i \) is equal to \( \log(1999!) \).

Step 2: Conclusion.
The correct answer is \( \log 1999! \), corresponding to option (4).