Question

Find the domain of the following function:

$\log \left(\sqrt{\frac{16}{x^2}}\right)$

Answer 1

$\log \left(\sqrt{\frac{16}{x^2}}\right)=\log \left(\sqrt{\frac{4^2}{x^2}}\right)=\log \left(\frac{4}{x}\right)$

The functon is defined only when

$\frac{4}{x}>0⟹x>0$

$x\in (0,\infty )$