Question
Which of the following logarithmic expressions is undefined?(1 point)
Responses
log3−9
log
3
−
9
logarithm subscript 3 baseline negative 9
log3.19.61
log
3.1
9.61
logarithm subscript 3.1 baseline 9.61
log39
log
3
9
logarithm subscript 3 baseline 9
log1.32.8561
Responses
log3−9
log
3
−
9
logarithm subscript 3 baseline negative 9
log3.19.61
log
3.1
9.61
logarithm subscript 3.1 baseline 9.61
log39
log
3
9
logarithm subscript 3 baseline 9
log1.32.8561
Answers
GPT-4o mini
To determine which logarithmic expression is undefined, we need to recall the properties of logarithms:
1. The logarithm of a non-positive number (zero or negative) is undefined.
2. Logarithms are defined for positive real numbers only.
Now, let's evaluate each expression:
1. \( \log_3(-9) \): This is undefined because the argument (−9) is negative.
2. \( \log_{3.1}(9.61) \): This is defined because both the base (3.1) and the argument (9.61) are positive.
3. \( \log_3(9) \): This is defined because both the base (3) and the argument (9) are positive.
4. \( \log_{1.32}(2.8561) \): This is defined because the base (1.32) is positive and greater than 1, and the argument (2.8561) is also positive.
Based on this analysis, the expression that is undefined is:
**\( \log_3(-9) \)**
1. The logarithm of a non-positive number (zero or negative) is undefined.
2. Logarithms are defined for positive real numbers only.
Now, let's evaluate each expression:
1. \( \log_3(-9) \): This is undefined because the argument (−9) is negative.
2. \( \log_{3.1}(9.61) \): This is defined because both the base (3.1) and the argument (9.61) are positive.
3. \( \log_3(9) \): This is defined because both the base (3) and the argument (9) are positive.
4. \( \log_{1.32}(2.8561) \): This is defined because the base (1.32) is positive and greater than 1, and the argument (2.8561) is also positive.
Based on this analysis, the expression that is undefined is:
**\( \log_3(-9) \)**