Why are the domains for \ln x^2 and 2\ln x

Gwendolyn Willett

Gwendolyn Willett

Answered question

2022-01-21

Why are the domains for lnx2 and 2lnx different?

Answer & Explanation

Daniel Cormack

Daniel Cormack

Beginner2022-01-21Added 34 answers

First, you could use lnx to define functions with different domains as long as lnx is defined in that domain.
Second, the rule lnxn=nlnx is a bit sloppy. It should always be pointed out that x>0. Likewise, lnab=lna+lnb, only if a,b>0.
Rita Miller

Rita Miller

Beginner2022-01-22Added 28 answers

Note that:
ln(x2)=2ln|x|2lnx
so the two functions are different and have different domains.
RizerMix

RizerMix

Expert2022-01-27Added 656 answers

he functions f(x)=2lnx and g(x)=lnx2 have different domains. The domain of f is (0,), and the domain of g is R0. But as you said, when x is in the domain of f and the domain of g, we have f(x)=g(x).

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