Which of the following logarithmic expressions is undefined?(1 point)Responseslog3−9logarithm subscript 3 baseline negative 9log0.2564logarithm subscript 0.25 baseline 64log2.56.25logarithm subscript 2.5 baseline 6.25log327logarithm subscript 3 baseline 27

Answer 1

To determine which logarithmic expression is undefined, we need to remember that the logarithm of a non-positive number is undefined. The logarithmic expression \(\log_b(a)\) is defined for \(a > 0\) and \(b > 0\) (with \(b \neq 1\)).

Now let's evaluate each of the given expressions:

1. \(\log_3(-9)\): This is undefined because the argument \(-9\) is negative.

2. \(\log_{0.25}(64)\): This is defined because \(64 > 0\), and \(0.25 > 0\) with \(0.25 \neq 1\).

3. \(\log_{2.5}(6.25)\): This is defined because \(6.25 > 0\), and \(2.5 > 0\) with \(2.5 \neq 1\).

4. \(\log_3(27)\): This is defined because \(27 > 0\), and \(3 > 0\) with \(3 \neq 1\).

So, the expression that is undefined is:

\(\log_3(-9)\).