Question

Solve the following inequality:
$\frac{{\log }^{2}x-3\log x+3}{\log x-1}<1$

Answer 1

$let\log x=z$

$\frac{z^2-3z+3-z+1}{z-1}<0$

$\frac{z^2-4z+4}{z-1}<0$

$\frac{{(z-2)}^2}{z-1}<0$

$\frac{1}{z-1}<0$

$z-1<0$

$z<1$

$\log x<1$

$x<2$