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Consider the graph of ln(x^2) and then consider the graph of 2ln(x), missing anything?

I was momentarily caught off guard by this until I realized that when we derive the property: ln(x^a)=aln(x), we choose the positive root.

Has anyone ever run into a situation where it was better to say that ln(x^2)=2ln|x| ?

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# A petite observation about logarithms

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