1) log₂28+2*log₂12-log₂63=log₂28+log₂12²-log₂63=log₂(28*144/63)=
=log₂(4032/63)=log₂64=log₂2⁶=6*log₂2=6.
2)
(log₂x)²-3*log₂x≤4 ОДЗ: x>0
Пусть log₂x=t ⇒
t²-3t≤4
t²-3t-4≤0
t²-3t-4=0 D=25
t₁=-1 t₂=4 ⇒
(t+1)(t-4)≤0
(log₂x+1)(log₂x-4)≤0
log₂x-4=0 log₂x=4 x₁=2⁴=16
log₂x+1=0 log₂x=-1 x₂=2⁻¹=1/2 ⇒
(x-1/2)(x-16)≤0
-∞____+____1/2____-____16____+____∞
x∈[1/2;16].
3)
log₃(2x+5)=4
2x+5=3⁴
2x+5=81
2x=76
x=38.