[CHAOS]

2.$log_{3\surd x }x + log_{3x}\surd x = 0$


$2log_{3\surd x}x + log_{3x}x = 0$

$ \frac{2logx}{log3 + (1/2)logx} + \frac{logx}{log3 + logx} = 0$

$a = log x ;$

$ \frac{2a}{log3 + a/2} + \frac{a}{log3 + a} = 0$

$\frac{4a}{2log3 + a} + \frac{a}{log3 + a} = 0$

$\because log x \geqslant 0 $

\therefore ส่วนเป็นบวกเสมอ

ค.ร.น. $4alog3 + 4a^2 + 2alog3 + a^2 = 0$

$5a^2 + 6alog3 = 0$

$a = 0 , \frac{-6log3}{5}$

$ \therefore logx = 0 \vee logx= \frac{-6log3}{5}$

$\therefore x=1 , 3^{\frac{-6}{5}}$