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Natural Logarithm of Negative Number
The natural logarithm function ln(x) is definedonly for x>0. So the natural logarithm of a negativenumber is undefined. The complex logarithmic function Log(z) isdefined for negative numbers too.
Correspondingly, why can't you ln a negative number?
If you raise a negative number to apositive number that's not an integer, but instead afraction or a decimal, you might end up with a negativenumber underneath a square root. So in summary, because thebase can only be a positive number, that means the argumentof the logarithm can only be a positive number.
| Rule name | Rule |
|---|---|
| ln of negative number | ln(x) is undefined when x ≤ 0 |
| ln of zero | ln(0) is undefined |
| ln of one | ln(1) = 0 |
| ln of infinity | lim ln(x) = ∞ ,when x→∞ |
Additionally, what does negative log mean?
Negative Logarithms A negative logarithm means how many times todivide by the number. We can have just one divide: Example: What islog8(0.125) ? Well, 1 ÷ 8 = 0.125, Solog8(0.125) = −1.
The real natural logarithm function ln(x) isdefined only for x>0. So the natural logarithm of zero isundefined.