# How to calculate logarithms of a negative numbers?

I know that log of negative number does not exist on the real axis. But what about the complex number. Can we figure out the log value of a negative number in terms of a complex number?

Note by Ankan Gope
5 years ago

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Complex numbers are really vast. They pop up in logs of negative numbers and also in stuff like arcsin(2)(REALLY!).

- 5 years ago

ln(-1)=(i)(pi) So from there you can use basic log properties to determine the value of other negative logs. For example ln(-15)=ln((15)(-1))=ln(15)+ln(-1)=ln(15)+(i)(pi) If you had a different base just use change of base to get it into natural logarithm form, I think. I'm not too sure where log properties stop working.

- 5 years ago