Question

Помогите решить 2log(log₃x) 3) > 1

Answer 1

$2\log(\log_{3}x\times3)>1$

ОДЗ:

$\left \{ {{\log_{3}x\times3>0} \atop {x>0}} \right.\Leftrightarrow\left \{ {{\left \{ {{\log_{3}x>0} \atop {x>0}} \right.} \atop {x>0}} \right.\Leftrightarrow\left \{ {{x>1} \atop {x>0}} \right.\Leftrightarrow x>1$

$2\log(\log_{3}x\times3)>1\\2\log(3\log_{3}x)>1\\\log(3\log_{3}x)>\frac{1}{2}\\3\log_{3}(x)>10^{\frac{1}{2}}\\3\log_{3}(x)>\sqrt{10}\\\log_{3}(x)>\frac{\sqrt{10}}{3}\\x>3^{\frac{\sqrt{10}}{3}$