No, it's simply not defined, as tiny-tim said. I'm assuming you're working with real numbers.DrCrowbar said:Hi Tim!
Ah... clumsy me. I knew that. I really did. Well, used to...
So if you have ln(-∞), is that essentially ∞ or -∞?
tiny-tim said:Hi DrCrowbar!
There is no such thing as the ln of a negative number.
(unless we're allowed complex numbers, in which case eg ln(-1) = πi)
DrCrowbar said:
DrCrowbar said:
tiny-tim said:No, that's ∞i
No, they are not equal. -ln(-∞) is undefined, while ln(∞) is equal to infinity.
-ln(-∞) is undefined because the natural logarithm function, ln(x), is only defined for positive real numbers. Since -∞ is not a positive real number, the function does not have a valid output.
Infinity is not a number, but rather a concept of something that is unbounded or without limit. In terms of logarithms, infinity represents the value of a function that continues to increase without bound. For example, ln(x) approaches infinity as x approaches infinity.
The logarithm function is the inverse of the exponentiation function. This means that if y = a^x, then x = loga(y). In other words, logarithms tell us what power (or exponent) we need to raise a base number to in order to get a given result.
Infinity is a fundamental concept in mathematics, used in many different areas such as calculus, number theory, and geometry. It allows us to work with and understand quantities that are unbounded or without limit, and helps us solve complex problems and make predictions about the behavior of functions and equations.