What is the restriction in logarithm | Log Definition | Log Restriction

Log or logarithm is basically derived from the exponential function.

Definition: If any number N is expressed in the form of a^x, where a > 0 and a ≠ 1, then the index ‘x’ is called the logarithm of the number N to the base a.

Thus, if N = a^x, then x = logₐN, where a > 0 and a ≠ 1. N is always +ve and x is a real number.

The restriction to log is that the base should be greater than 0 and the base should not be 1. N should always be positive. x is a real number (+ve, 0 or -ve).

While the value of a log itself can be positive or negative, the base of the logarithmic function and the argument of the log function are different stories. The argument of a log function can only take positive arguments. In other words, the only numbers you can plug into a log function are positive numbers. Base, as explained above, should be > 0 and ≠ 1.

log 0 is undefined and log 1 is 0.