Question

Find the domain of definition of the following function:
$y=\log ({\log }^{2}x-5\log x+6).$

Answer 1

${\log }^{2}x-5\log x+6>0$ and $x>0$

$(\log x-3)(\log x-2)>0x\in (-\infty ,100)\cup (1000,\infty )$

Taking intersection, we get

$x\in (0,100)\cup (1000,\infty )$