Question

Реши уравнение
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Answer 1

$\displaystyle\bf\\2\log_{4} ^{2} x=12\log_{4} x-16\\\\2\log_{4} ^{2} x-12\log_{4} x+16=0\\\\\log_{4} ^{2} x-6\log_{4} x+8=0\\\\\log_{4} x=m\\\\m^{2} -6m+8=0\\\\Teorema \ \ Vieta :\\\\1) \ m_{1} =\boxed2 \ \ ; \ \ m_{2} =\boxed4\\\\2)\\\\\log_{4} x=2\\\\x_{1} =\boxed{16}\\\\\log_{4} x=4\\\\x_{2} =\boxed{256}$