Question

Помогите!!прошу решите хоть одно

Answer 1

a) ОДЗ : x > 0

$log_{2}^{2}x-9log_{8}x=4\\\\log_{2}^{2}x-9*\frac{1}{3}log_{2}x-4=0\\\\log_{2}^{2}x-3log_{2}x-4=0\\\\log_{2}x=m\\\\m^{2}-3m-4=0\\\\m_{1}=4\\\\m_{2}=-1\\\\log_{2}x=4\\\\x_{1}=16\\\\log_{2}x=-1\\\\x_{2}=0,5$

Ответ : 0,5 ; 4

б)

$2^{x^{2} }*(\frac{1}{2})^{\frac{1}{4}x }=\sqrt[4]{8}\\\\2^{x^{2} }*2^{-\frac{1}{4}x }=2^{\frac{3}{4} }\\\\2^{x^{2} -\frac{1}{4}x }=2^{\frac{3}{4} }\\\\x^{2}-\frac{1}{4}x=\frac{3}{4}\\\\4x^{2}-x-3=0\\\\D=(-1)^{2}-4*4*(-3)=1+48=49=7^{2}\\\\x_{1}=\frac{1+7}{8}=1\\\\x_{2}=\frac{1-7}{8}=-0,75$

Ответ : - 0,75 ; 1