Question

(㏒₃ˣ)² + ㏒₃ˣ - 2 = 0

Answer 1

${( log_{3}x) }^{2} + log_{3}(x) - 2 = 0$

$x>0$

$log_{3}(x) = t \: ,t > 0$

${t}^{2} + t - 2 = 0$

${t}^{2} + 2t - t - 2 = 0$

$t(t + 2) - (t + 2) = 0$

$(t + 2)(t - 1) = 0$

$t + 2 = 0 = > t = - 2 \: nu \: convine$

$t - 1 = 0 = > t = 1$

$= > log_{3}(x) = 1 = > x = 3$