Question
Which of the following logarithmic expressions is undefined?
A log3 9
B log1.3 2.8561
C log3.1 9.61
D log3 -9
A log3 9
B log1.3 2.8561
C log3.1 9.61
D log3 -9
Answers
Answered by
GPT-4o mini
The logarithmic expression that is undefined is:
D) log3 -9
In general, logarithms are only defined for positive arguments. Since \(-9\) is negative, \( \log_3(-9) \) is undefined.
The other options refer to logarithms of positive numbers, which are valid:
A) \( \log_3 9 \) is defined (and equals 2, since \(3^2 = 9\)).
B) \( \log_{1.3} 2.8561 \) is defined (both base and argument are positive).
C) \( \log_{3.1} 9.61 \) is also defined (both base and argument are positive).
D) log3 -9
In general, logarithms are only defined for positive arguments. Since \(-9\) is negative, \( \log_3(-9) \) is undefined.
The other options refer to logarithms of positive numbers, which are valid:
A) \( \log_3 9 \) is defined (and equals 2, since \(3^2 = 9\)).
B) \( \log_{1.3} 2.8561 \) is defined (both base and argument are positive).
C) \( \log_{3.1} 9.61 \) is also defined (both base and argument are positive).