Question

Which of the following logarithmic expressions is properly defined?

A. log
7
​
(−49)
B. log
1
​
(100)
C. log
3
​
(
3
1
​
)
D. log
2
​
(1)

Answer 1

A logarithm log_b(a) is defined (as a real number) only when b>0, b≠1, and a>0.

A. log_7(−49): argument −49 ≤ 0 → not defined.
B. log_1(100): base 1 → not allowed.
C. log_3(3/1) (or log_3(3)): base 3>0, ≠1, argument >0 → defined (equals 1).
D. log_2(1): base 2>0, ≠1, argument 1>0 → defined (equals 0).

So C and D are properly defined.