Question

1. which of the following logarithmic expressions is undefined? (5 points)\\(\log_{3} -9\\)\\(\log_{3} 27\\)\\(\log_{0.25} 64\\)\\(\log_{2.5} 6.25\\)

Explanation:

Step1: Recall log domain rule

A logarithmic expression $\log_b a$ is defined only if $a>0$, $b>0$, and $b
eq1$.

Step2: Check each option

• $\log_3 -9$: The argument $-9<0$, violates the domain rule.
• $\log_3 27$: $3>0,3

eq1,27>0$, defined.

• $\log_{0.25} 64$: $0.25>0,0.25

eq1,64>0$, defined.

• $\log_{2.5} 6.25$: $2.5>0,2.5

eq1,6.25>0$, defined.

Answer:

$\log_3 -9$