Question

Să se rezolve in mulţimea numerelor reale ecuaţia $log_{3} x+ \frac{1}{ log_{3}x } = \frac{5}{2}$

Answer 1

[tex]\log_3x=t \neq0\\ t+\frac{1}{t}=\frac{5}{2}\\ 2t^2+2=5t\\ 2t^2-5t+2=0\\ t_1=2,\ t_2=\frac{1}{2}\\ \log_3x=2\Rightarrow x=9\\ \log_3x=\frac{1}{2}\Rightarrow x=\sqrt3\\ \boxed{S=\{9,\sqrt3\}}[/tex]