Question
Which of the following logarithmic expressions is undefined?
(1 point)
Responses
log3−9
log sub 3 minus 9
log0.2564
the log base 0 point 2 5 of 64
log2.56.25
the log base 2 point 5 of 6 point 2 5
log327
(1 point)
Responses
log3−9
log sub 3 minus 9
log0.2564
the log base 0 point 2 5 of 64
log2.56.25
the log base 2 point 5 of 6 point 2 5
log327
Answers
Answered by
GPT-4o mini
To determine which of the logarithmic expressions is undefined, we need to analyze each option:
1. **log₃(-9)**: The logarithm of a negative number is undefined in the real number system. Therefore, this expression is undefined.
2. **log₀.₂₅(64)**: Logarithms with a base less than or equal to zero or equal to one are also undefined in the real number system. Since 0.25 is less than 1, this expression is also undefined.
3. **log₂.₅(6.25)**: This expression is valid since the base (2.5) is greater than 1, and the argument (6.25) is positive.
4. **log₃(27)**: This expression is valid as both the base (3) and the argument (27) are positive, and the base is not equal to 1.
Based on this analysis, the two logarithmic expressions that are undefined are:
- log₃(-9)
- log₀.₂₅(64)
However, if you need to choose only one undefined expression from the provided options, log₃(-9) is clearly the most straightforward choice since logarithms of negative numbers are universally undefined.
1. **log₃(-9)**: The logarithm of a negative number is undefined in the real number system. Therefore, this expression is undefined.
2. **log₀.₂₅(64)**: Logarithms with a base less than or equal to zero or equal to one are also undefined in the real number system. Since 0.25 is less than 1, this expression is also undefined.
3. **log₂.₅(6.25)**: This expression is valid since the base (2.5) is greater than 1, and the argument (6.25) is positive.
4. **log₃(27)**: This expression is valid as both the base (3) and the argument (27) are positive, and the base is not equal to 1.
Based on this analysis, the two logarithmic expressions that are undefined are:
- log₃(-9)
- log₀.₂₅(64)
However, if you need to choose only one undefined expression from the provided options, log₃(-9) is clearly the most straightforward choice since logarithms of negative numbers are universally undefined.