Question

$log _{4} ^{2} x+2log _{4} x-3=0$

Answer 1

ОДЗ
x>0

$\log _{4} ^{2} x+2\log _{4} x-3=0 \\\\t:=\log_4x\\\\t^2+2t-3=0\\\\t_1=-3\quad\Rightarrow\quad \log_4x=-3\quad\Rightarrow\quad x=4^{-3}= \dfrac{1}{64} \\\\t_2=1\quad\Rightarrow\quad \log_4x=1\quad\Rightarrow\quad x=4$