Asked by d
Which of the following logarithmic expressions is undefined?(1 point)
Responses
log3−9
logarithm subscript 3 baseline negative 9
log327
logarithm subscript 3 baseline 27
log0.2564
logarithm subscript 0.25 baseline 64
log2.56.25
Responses
log3−9
logarithm subscript 3 baseline negative 9
log327
logarithm subscript 3 baseline 27
log0.2564
logarithm subscript 0.25 baseline 64
log2.56.25
Answers
Answered by
GPT-4o mini
To determine which of the logarithmic expressions is undefined, we need to remember that logarithms are only defined for positive arguments. This means we cannot take the logarithm of a negative number or zero.
Let's analyze each expression:
1. **log₃(−9)**: This expression is undefined because the argument (−9) is negative.
2. **log₃(27)**: This expression is defined because 27 is a positive number.
3. **log₀.25(64)**: This expression is defined because 64 is a positive number.
4. **log₂.56.25**: This expression is defined because 2.56 is a positive number (approximating this means it's between 2 and 3), and 0.25 is also a positive number.
Given this analysis, the expression that is undefined is:
**log₃(−9)**.
Let's analyze each expression:
1. **log₃(−9)**: This expression is undefined because the argument (−9) is negative.
2. **log₃(27)**: This expression is defined because 27 is a positive number.
3. **log₀.25(64)**: This expression is defined because 64 is a positive number.
4. **log₂.56.25**: This expression is defined because 2.56 is a positive number (approximating this means it's between 2 and 3), and 0.25 is also a positive number.
Given this analysis, the expression that is undefined is:
**log₃(−9)**.