Question

why logathem is undefined on negative numbers​

Answer 1

Answer:

See explanation.

Step-by-step explanation:

log a to the base b = c implies that b^c = a

This is the primary definition of a logarithm. The base is always a positive number. The base could be any number. However, "10" is popularly used and such logarithms are called common logarithms.

Observe that b^c will always be a positive number because "b" itself is positive. No matter what the value of "c" is (even if it is negative), b^c cannot be negative. Hence "a" which is equal "b^c" by definition will always be a positive number.

Hence, we cannot have "log a" where a is negative simply because you cannot have "b" and "c" (as explained above) such that b^c = a. The definition of logarithm does not hold true for a negative value of "a", which is why log of a negative number is undefined.

Hope this has helped give you a broad understanding!