Question

Помогите решить 2log(log₃x) 3) > 1

Answer 1

$2log(log_{3}xtimes3)>1$

ОДЗ:

$left { {{log_{3}xtimes3>0} atop {x>0}} right.Leftrightarrowleft { {{left { {{log_{3}x>0} atop {x>0}} right.} atop {x>0}} right.Leftrightarrowleft { {{x>1} atop {x>0}} right.Leftrightarrow x>1$

$2log(log_{3}xtimes3)>1\2log(3log_{3}x)>1\log(3log_{3}x)>frac{1}{2}\3log_{3}(x)>10^{frac{1}{2}}\3log_{3}(x)>sqrt{10}\log_{3}(x)>frac{sqrt{10}}{3}\x>3^{frac{sqrt{10}}{3}$