Question
Which of the following logarithmic expressions is undefined?(1 point) Responses log39 the log base 3 of 9 log1.32.8561 the log base 1 point 3 of 2 point 8 5 6 1 log1.39.61 the log base 1 point 3 of 9 point 6 1 log3−9 log sub 3 minus 9
Answers
Answered by
GPT-4o mini
A logarithmic expression is undefined for certain bases and arguments. The logarithm \(\log_b(a)\) is undefined if:
1. The base \(b\) is less than or equal to 0 or equal to 1.
2. The argument \(a\) is less than or equal to 0.
Now let's analyze each option:
1. **\(\log_3(9)\)** - This is defined because 3 (base) is greater than 1 and 9 (argument) is positive.
2. **\(\log_{1.3}(2.8561)\)** - This is defined because 1.3 (base) is greater than 1 and 2.8561 (argument) is positive.
3. **\(\log_{1.3}(9.61)\)** - This is also defined for the same reason as above.
4. **\(\log_3(-9)\)** - This is **undefined** because the argument -9 is less than 0.
Thus, the expression that is undefined is:
\(\log_3(-9)\)
1. The base \(b\) is less than or equal to 0 or equal to 1.
2. The argument \(a\) is less than or equal to 0.
Now let's analyze each option:
1. **\(\log_3(9)\)** - This is defined because 3 (base) is greater than 1 and 9 (argument) is positive.
2. **\(\log_{1.3}(2.8561)\)** - This is defined because 1.3 (base) is greater than 1 and 2.8561 (argument) is positive.
3. **\(\log_{1.3}(9.61)\)** - This is also defined for the same reason as above.
4. **\(\log_3(-9)\)** - This is **undefined** because the argument -9 is less than 0.
Thus, the expression that is undefined is:
\(\log_3(-9)\)