Question

log(3)x+log(x)9=3?????????

Answer 1

$log_{3}x+log_{x}9 = 3\ log_{3}x+frac{1}{log_{3^{2}}x} = 3\ log_{3}x+frac{2}{log_{3}x} = 3\ frac{(log_{3}x)^{2}+2}{log_{3}x} = 3\ (log_{3}x)^{2}+2 = 3log_{3}x\ log_{3}x = t\ t^{2} - 3t +2 = 0\ t_{1}=1, t_{2}=2\ log_{3}x =1, log_{3}x =2 \ x=3, x=9$