Question

Логарифмическое неравенство
log2^2 (x-1) - log0.5 (x-1) >2

Answer 1

log²₂(x-1)-log₀,₅(x-1)>2
ОДЗ: x-1>0; x>1
log²₂(x-1)+log₂(x-1)-2>0
[log₂(x-1)+2][log₂(x-1)-1]>0 __+__-2__-___1__+__
1) log₂(x-1)<-2
x-1<2⁻²=1/4
x<1+1/4=5/4=1.25
2) log₂(x-1)>1
x-1>2
x>3
x∈(1;1.25)∪(3:∞)