Question

Solve the following inequality:

${\left(\frac{x}{10}\right)}^{\log x-2}<100$

Answer 1

${\left(\frac{x}{100}\right)}^{\log x-2}<100$

$(\log x-2)\log \left(\frac{x}{10}\right)<\log 100$

$(\log x-2)(\log x-1)<2$

${\left(\log x\right)}^2-3\log x+2<2$

${\left(\log x\right)}^2-3\log x<0$

$\left(\log x\right)-(\log x-3)<0$

$\log xϵ(0,3)$

$xϵ(1,1000)$