Question

помогите пожалуйста!! Решите два уравнения:​

Answer 1

$\displaystyle\bf\\1)\\\\\log_{3} ^{2} x-12\log_{3} x+27=0\\\\ODZ \ : \ x > 0\\\\\log_{3} x=m\\\\m^{2} -12m+27=0\\\\D=(-12)^{2} -4\cdot27=144-108=36=6^{2} \\\\\\m_{1}=\frac{12-6}{2} =\frac{6}{2} =3\\\\\\m_{2} =\frac{12+6}{2} =\frac{18}{2} =9\\\\\\\log_{3} x=3\\\\x_{1} =3^{3} =27\\\\\\\log_{3} x=9\\\\x_{2} =3^{9} =19683\\\\\\Otvet \ : \ 27 \ ; \ 19683$

$\displaystyle\bf\\2)\\\\2\log_{4} ^{2} x-5\log_{4} x+2=0\\\\ODZ \ : \ x > 0\\\\\log_{4} x=m\\\\2m^{2} -5m+2=0\\\\D=(-5)^{2} -4\cdot 2\cdot 2=25-16=9=3^{2} \\\\\\m_{1} =\frac{5-3}{4} =\frac{2}{4} =\frac{1}{2} \\\\\\m_{2} =\frac{5+3}{4} =\frac{8}{4} =2\\\\\\\log_{4} x=\frac{1}{2} \\\\x_{1} =4^{\frac{1}{2} } =\sqrt{4} =2\\\\\log_{4} x=2\\\\x_{2} =4^{2} =16\\\\\\Otvet \ : \ 2 \ ; \ 16$