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, 201312 yr by Acnhduy

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.

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).

Thanks all

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.