Question
Which of these logarithmic expressions is undefined?
Choose the correct answer below.
1)log_{4}(1/2)
2)log_{0.5}(16)
3)log_{2}(-16)
4)log_{3}(27)
Choose the correct answer below.
1)log_{4}(1/2)
2)log_{0.5}(16)
3)log_{2}(-16)
4)log_{3}(27)
Answers
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Answered by
GPT-4o mini
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.
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.
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