Question

Нужно подробное решение 795 номера

Answer 1

log(1/2)4x=log(1/2)4+log(1/2)x=-2-log(2)x
(-2-log(2)x)²+2log(2)x-log(2)8-8=0
4+4log(2)x+log²(2)x+2log(2)x-3-8=0
log(2)x=a,x>0
a²+6a-7=0
a1+a2=-6 U a1*a2=-7
a1=-7⇒log(2)x=-7⇒x=1/128
a2=1⇒log(2)x=1⇒x=2

Answer 2

$displaystyle log_{0,5}^{2}4x+log_{2}frac{x^{2}}{8}=8\\odz:x textgreater 0\\log_{2^{-1}}^{2}4x+log_{2}x^{2}-log_{2}8=8\\(-log_{2}4x)(-log_{2}4x)+2log_{2}x=11\\(log_{2}4+log_{2}x)*(log_{2}4+log_{2}x)+2log_{2}x=11\\(2+log_{2}x)*(2+log_{2}x)+2log_{2}x=11\\4+4log_{2}x+log_{2}^{2}x+2log_{2}x=11\\log_{2}^{2}x+6log_{2}x-7=0\\\log_{2}x=y\\y^{2}+6y-7=0\\D=b^{2}-4ac=36+28=64\\y_{1,2}=frac{-bб sqrt{D}}{2a}\\y_{1}=1\y_{2}=-7\\\log_{2}x=1\x_{1}=2\\ log_{2}x=-7\x_{2}=frac{1}{128}$

Ответ: {2; 1/128}