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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

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    $\begingroup$ What makes you think that $-x$ is negative? $\endgroup$ Jan 11 at 0:44
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    $\begingroup$ $-x$ could be positive if $x$ is negative! $\endgroup$ Jan 11 at 0:58
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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 $\text{log}(-x)$?

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