1) log2^2(1-x)-2log2(1-x)=3 2) 2 log2x=3log3x 3) 2log2x-5logx2=3

Question

1) log2^2(1-x)-2log2(1-x)=3
2) 2 log2x=3log3x
3) 2log2x-5logx2=3

Answer 1

1)
log₂²(1-x)-2log₂(1-x)=3     1-x>0   x<1<br>log₂(1-x)=t  ⇒
t²-2t-3=0  D=16
t₁=3    t₂=-1 
log₂(1-x)=3  1-x=2³   1-x=8   x₁=-7
log₂(1-x)=-1   1-x=2⁻¹   1-x=0,5   x₂=0,5