3 Which of the following logarithmic expressions is undefined?
(A)
(B)
©
(D)

Ask by Logan Gray. in the United States

Mar 24,2025

Question

3 Which of the following logarithmic expressions is undefined? (A) $$ \log _{3} 9 $$ (B) $$ \log _{1.3} 2.8561 $$ (C) $$ \log _{3.1} 9.61 $$ (D) $$ \log _{2}-5 $$

UpStudy AI · Accepted Answer

1. Recall that for the logarithmic expression $$ \log_b a $$ to be defined, the base $$ b $$ must satisfy $$ b > 0 $$ and $$ b 
eq 1 $$, and the argument $$ a $$ must satisfy $$ a > 0 $$.

2. For option (A) $$ \log_{3} 9 $$:
   - Base: $$ 3 > 0 $$ and $$ 3 
eq 1 $$
   - Argument: $$ 9 > 0 $$
   - This expression is defined.

3. For option (B) $$ \log_{1.3} 2.8561 $$:
   - Base: $$ 1.3 > 0 $$ and $$ 1.3 
eq 1 $$
   - Argument: $$ 2.8561 > 0 $$
   - This expression is defined.

4. For option (C) $$ \log_{3.1} 9.61 $$:
   - Base: $$ 3.1 > 0 $$ and $$ 3.1 
eq 1 $$
   - Argument: $$ 9.61 > 0 $$
   - This expression is defined.

5. For option (D) $$ \log_{2} (-5) $$:
   - Base: $$ 2 > 0 $$ and $$ 2 
eq 1 $$
   - Argument: $$ -5 $$ 
   - Since $$ -5 $$ is not greater than $$ 0 $$, the logarithm is undefined.

The only expression that is undefined is option (D) $$ \log_{2} (-5) $$.
Option (D) $$ \log_{2} (-5) $$ is undefined.

3 Which of the following logarithmic expressions is undefined?
(A)
(B)
©
(D)

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3 Which of the following logarithmic expressions is undefined? (A) (B) © (D)