The logarithm function, specifically log x, is undefined for any values of x that are less than or equal to zero. This is because logarithms are only defined for positive real numbers.
In mathematical terms, the logarithm represents the power to which a base number (typically 10 or e) must be raised to produce a given number. For example, log10(100) = 2 because 102 = 100. However, there are no real numbers that you can raise to a power to get a zero or a negative number.
To summarize, log x is undefined for:
- x ≤ 0
Therefore, the only valid input for the logarithmic function is any positive number (x > 0).