Question

Решите пж уравнение

$log_{3} {(x - 3)}^{2} + log_{3} |x - 3| = 3$
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Answer 1

$\log_3(x-3)^2+\log_3|x-3|=3$

$2\log_3|x-3|+\log_3|x-3|=3$

ОДЗ: $x-3\neq 0\Rightarrow x\neq 3$

$3\log_3|x-3|=3|:3\\\\\log_3|x-3|=1,\\\\|x-3|=3^1\\\\|x-3|=3\Leftrightarrow \left \ [ {{x-3=3} \atop {x-3=-3}} \right. \left \ [ {{x=6} \atop {x=0}} \right.$

ОТВЕТ: {0, 6}.