Question

Explore the limitations of the values of b and x in equations of the form logbx=L
by determining which logarithm is undefined.(1 point)

log1319


log2.56.25


log51


log50

Answer 1

A logarithm log_b(x) is defined only when b>0, b≠1, and x>0.

Evaluate each:
- log_13 19: base 13>0, ≠1; argument 19>0 → defined.
- log_{2.5} 6.25: base 2.5>0, ≠1; argument 6.25>0 → defined (in fact 2.5^2 = 6.25 so the value is 2).
- log_5 1: base 5 OK, argument 1>0 → defined (value 0).
- log_5 0: argument 0 is not >0 → undefined.

So only log_5 0 is undefined.