Domain of $2\log_2x$ and $\log_2x^2$

Question

Domain of $2\log_2x$ and $\log_2x^2$

For $2\log_2x$ domain is simply $x>0$
For$\log_2x^2$ domain may be $R$ , I think so. Is am I right or wrong .

Answer 1

If you call “domain” of an expression the set of real numbers for which it makes sense (as a real number), then, yes, the domain of $2\log_2x$ is $\{x\in\mathbb R\mid x>0\}$. But the domain of $\log_2x^2$ is $\mathbb R\setminus\{0\}$.