Question

can some one explain
why the modulus of the argument for a logarithm is sometimes used
\(\log |x|\)

Answer 1

havent worded this question very well

Answer 2

You mean the absolute value? Because logarithm is undefined for x<0

Answer 3

yeah exactly , wouldn't taking the modulus mean some extra solutions creep in?

Answer 4

Yup. That means the argument of the log is always '+ve', 'cause it's in a mod.

So, the negative part of the 'x-axis' can also be included in the domain of the log.

The graph can now be: