Product rule for logarithms works on any non-zero value?
The product rule for logarithms states
broggesy9
Answered question
2022-04-28
Product rule for logarithms works on any non-zero value? The product rule for logarithms states that: Most sources that I've found* state that this rule only applies when M and N are positive. It's true that is undefined, but negative values in place of M and N seem to work just fine: Why the discrepancy?
Answer & Explanation
Draidayerabauu
Beginner2022-04-29Added 9 answers
Try this in Wolframalpha. This will give you the result is false. The reason being log in the true sense is a multi-valued function. This is due to the fact that any can also be written as , where . This results in a multi-valued logarithm function. For instance, where and denotes the real value However, if we restrict our domain to positive reals, and say we are only interested in real valued logarithm, then we have where It is also important to note that the imaginary part of is an integer multiple of if and only if z is a positive real number.
Alice Harmon
Beginner2022-04-30Added 12 answers
Nonsense. Don't trust software blindly. W|A is using the complex logarithm, which is a multi-valued function (meaning that it can give you a value for the log of any nonzero complex number, but it's not the logarithm, and not all of the properties that you expect will hold without caveats). By definition, Since for all as a function of a real variable, is only defined for