Question

Aflati x din egalitatea: $log_{3}x+1=2 log_{x}3$. Mersi.

Answer 1

$x\ \textgreater \ 0,\ x\neq1$

$log_3x=\dfrac{1}{log_x3}$

Notam:  $a=log_x3$

Obtinem:

$\dfrac1a+1=2a\Rightarrow a\in\{1;\ -\dfrac12\}$

$log_x3=1\Rightarrow x=3$

$log_x3=-\dfrac12\Rightarrow x^{-\frac12}=3\Rightarrow x=3^{-2}=\dfrac19$