Log2(1-х) +log2(-5х-2)=2+log2 3

Question

Log2(1-х) +log2(-5х-2)=2+log2 3

Answer 1

ОДЗ: 0} \atop {-5x-2>0}} \right. " alt=" \left \{ {{1-x>0} \atop {-5x-2>0}} \right. " align="absmiddle" class="latex-formula">

log₂(-5x-2+5x²+2x)=log₂4+log₂3
log₂(5x²-3x-2)=log₂12
5x²-3x-2=12
5x²-3x-14=0
D=9+280=289
√D=17
x₁=2 ∉ ОДЗ
x₂=-1,4