1. log₂(x²-15x)=2
x-15x²=4
x²-15-4=0 D=241
x₁,₂=(15+/-√241)/2).
2. lg(x-1)-lg(2x-11)=lg2
lg(x-1)=lg(2*(2x-11))
x-1=4x-22
x=7.
3. log₃²x-log₂x=2
log₃x=v>0
v²-v-2=0 D=9
v₁=2 v₂=-1 v₂∉
log₃x=2
x=9
4.log₂(x-5)≤2
x-5≤4
x≤9. x∈[-∞;9].
5. log₃(5-4x)(5-4x)/(x-1)<0<br>-∞____-____1____+____1,25____-____+∞ ⇒
x∈(-;∞1)∨(1,25;+∞)
6. lgx-lgy=2 x/y=100 x=100y x=1000
x-10y=900 x-10y=900 100y-10y=900 y=10.