Which of the following logarithmic expressions is undefined?(1 point)

Question

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

Answer 1

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:

\( \log_3(-9) \)