Negative log?

[Acnhduy]

Why is it not possible to have the log of a negative number?
Examples would be greatly appreciated.

Furthermore, is it the base that cannot be negative?

Like log_-bx

or is it that when you have a number and you log it, the number cannot be negative. log(-x)

Edited October 4, 2013 by Acnhduy

[studiot]

Draw a graph of y = log x (any base)

 

Note that the graph does not cross the y axis or it does not enter the region where x<0.

All values of the log graph appear on this line and nowhere else on the graph.

 

This is the same as for a square root. Are you suprised there are not square roots of negative numbers?

 

 

This is true of all graphs. They show the only values of the expression.

[timo]

The logarithm is usually considered as the inverse of the exponential function over the reals. Since exp(x) is never negative for any x, the logarithm of a negative number can never be a real number. It is principally possible to consider the logarithm as a sort of inverse of the exponential function over the complex numbers. Since exp(i*Pi)=-1, one could argue thatm log(-1) should equal i*Pi. This is sometimes done (Mathematica treats the log like that by default, I believe) but comes with some other problems (related to why I said sort of inverse one sentence before).

[Acnhduy]

Thanks all

[Olinguito]

Why is it not possible to have the log of a negative number?

Are you suprised there are not square roots of negative numbers?

Logarithms and square roots of negative numbers do exist. They are complex rather than real.