Question

Solve the following equation:
${\log }_{\frac{1}{3}}x-3\sqrt{{\log }_{\frac{1}{3}}x}+2=0$

Answer 1

${\log }_{\frac{1}{3}}x-3\sqrt{{\log }_{\frac{1}{3}}x}+2=0Let{\log }_{\frac{1}{3}}x=a.a-3\sqrt{a}+2=0\Rightarrow (\sqrt{a}-1)(\sqrt{a}-2)=0\Rightarrow \sqrt{a}=1,2\Rightarrow a=1,4.\Rightarrow x=\frac{1}{3},{\left(\frac{1}{3}\right)}^4\Rightarrow x=\frac{1}{3},\frac{1}{81}.$