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?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Comments

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.

Grant Elliot - 8 years ago

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

Nishant Rai - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$