Log ^2(0.5)4x + log(2) x^2/8=8 решите , 11 класс - вопрос №66601052054228811 от liza2002623 28.05.2021 16:36

Question

Алгебра: Log ^2(0.5)4x + log(2) x^2/8=8 решите , 11 класс

liza2002623 · Answer

Log(0,5)4x=log(0,5)x+log(0,5)4=log(0,5)x-2
log(2)(x²/8)=log(20x²-log(2)8=2log(2)x-3=log(0,5)x/log(0,5)2 -3=-2log(0,5)x-3

(log(0,5)-2)²-2log(0,5)x-3-8=0
log²(0,5)x-4log(0,5)x+4-2log(0,5)x-11=0
log²(0,5)x-6log(0,5)x-7=0
log(0,5)x=a
a²-6a-7=0
a1+a2=6 U a18a2=-7
a1=7⇒log(0,5)x=7⇒x=1/128
a2=-1⇒log(0,50x=-1⇒x=2