Which of these logarithmic expressions is undefined?

Question

Choose the correct answer below.
1)log_{4}(1/2)
2)log_{0.5}(16)
3)log_{2}(-16)
4)log_{3}(27)

Answer 1

To determine which of the logarithmic expressions is undefined, we can evaluate each option:

1. \( \log_{4}(1/2) \):

   • This is defined. The logarithm of a positive number (like \( 1/2 \)) to a positive base (like \( 4 \)) is defined.

2. \( \log_{0.5}(16) \):

   • This is also defined. The base \( 0.5 \) is a positive number less than \( 1 \), and \( 16 \) is positive. So, this expression is defined.

3. \( \log_{2}(-16) \):

   • This expression is undefined because the logarithm of a negative number is not defined in the real number system.

4. \( \log_{3}(27) \):

   • This is defined. Here, \( 27 \) is positive, and so is the base \( 3 \). Therefore, this expression is defined.

Based on the evaluations, the answer is:

3) log_{2}(-16) is undefined.