Question

Будь ласка...
log3^2x+log1/3x+2=0​

Answer 1

ОДЗ : x > 0

$log_{3^{2}}x+log_{\frac{1}{3}}x+2=0\\\\log_{(3^{2})^{\frac{1}{2}}}x^{\frac{1}{2}}+log_{(\frac{1}{3})^{-1} }x^{-1} +2=0\\\\\frac{1}{2}log_{3}x-log _{3}x+2=0\\\\-\frac{1}{2}log_{3}x=-2\\\\log_{3}x=4\\\\x=3^{4}=81\\\\Otvet:\boxed{81}$