when you have the expression $\log( -x)$ base $3$, isn't that undefined, because you can't raise 3 to any power which will give you a negative value?

I am supposed to graph this expression and from the transformation of functions, this makes sense though because you just flip the graph of $log x$ base $3$ over the y-axis.

I would like to know why you get two different answers?

Thanks, Amruth

  • 3
    $\begingroup$ What makes you think that $-x$ is negative? $\endgroup$ Jan 11 at 0:44
  • 3
    $\begingroup$ $-x$ could be positive if $x$ is negative! $\endgroup$ Jan 11 at 0:58

Since $\log(x)$ is only defined on $(0,\infty)$ we get that $\log(-x)$ is only defined on $(-\infty, 0)$ Morever, given $f(x) = \log(x)$, we get that $f(-x) = \log(-x)$ is the reflection about the y-axis.

Hence, we do not get two answers from the same input of the given function. That is to say : $\log$ is a well-defined function.

Also see here : What is $\text{log}(-x)$?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.