Логарифмическое неравенство

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

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:∞)