Question
Which of the following logarithmic expressions is undefined?(1 point)
Responses
log3−9
log
3
−
9
log sub 3 minus 9
log2.56.25
log
2.5
6.25
the log base 2 point 5 of 6 point 2 5
log327
log
3
27
the log base 3 of 27
log0.2564
Responses
log3−9
log
3
−
9
log sub 3 minus 9
log2.56.25
log
2.5
6.25
the log base 2 point 5 of 6 point 2 5
log327
log
3
27
the log base 3 of 27
log0.2564
Answers
Answered by
GPT-4o mini
To determine which logarithmic expressions are undefined, we need to remember that the logarithm of a negative number or zero is undefined.
Let's go through the options:
1. **log3−9**: This is log base 3 of -9, which is undefined because you cannot take the logarithm of a negative number.
2. **log2.56.25**: This is log base 2.5 of 6.25, which is defined since both arguments are positive.
3. **log327**: This is log base 3 of 27. This is defined since both 3 and 27 are positive.
4. **log0.2564**: This is log base 0.25 of 64. In this case, the base (0.25) is positive and less than 1, and the argument (64) is positive, making this logarithmic expression defined.
From the analysis above, the expression that is undefined is:
**log3−9 (log base 3 of -9)**.
Let's go through the options:
1. **log3−9**: This is log base 3 of -9, which is undefined because you cannot take the logarithm of a negative number.
2. **log2.56.25**: This is log base 2.5 of 6.25, which is defined since both arguments are positive.
3. **log327**: This is log base 3 of 27. This is defined since both 3 and 27 are positive.
4. **log0.2564**: This is log base 0.25 of 64. In this case, the base (0.25) is positive and less than 1, and the argument (64) is positive, making this logarithmic expression defined.
From the analysis above, the expression that is undefined is:
**log3−9 (log base 3 of -9)**.